%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV063^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n100.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:41 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV063^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n100.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:51:41 CDT 2014
% % CPUTime  : 300.10 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1bd5950>, <kernel.Type object at 0x1bd50e0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xz))))) of role conjecture named cTHM136_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xz))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xz)))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xy)))) (forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xy) Xz))))->(forall (Xp:(a->(a->Prop))), (((and (forall (Xx0:a) (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((Xp Xx0) Xz0))))->((Xp Xx) Xz)))))
% Found x4:((Xp Xx0) Xz)
% Found (fun (x5:((Xp Xy0) Xz))=> x4) as proof of ((Xp Xx0) Xz)
% Found (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect10 (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect1 ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4)) as proof of ((Xp Xx0) Xz)
% Found (fun (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x4:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((Xp Xx0) Xz)) (x5:((Xp Xy0) Xz))=> x4))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x5:((Xp Xx) Xz0)
% Found (fun (x5:((Xp Xx) Xz0))=> x5) as proof of ((Xp Xx) Xz0)
% Found (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect10 (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect1 ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5)) as proof of ((Xp Xx) Xz0)
% Found (fun (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x4:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((Xp Xx) Xy0)) (x5:((Xp Xx) Xz0))=> x5))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x7:((Xp Xx) Xz0)
% Found (fun (x7:((Xp Xx) Xz0))=> x7) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x6:((Xp Xx0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x6) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x6:((Xp Xx0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x6) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x7:((Xp Xx) Xz0)
% Found (fun (x7:((Xp Xx) Xz0))=> x7) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x7:((Xp Xx) Xz0)
% Found (fun (x7:((Xp Xx) Xz0))=> x7) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xz0)->((Xp Xx) Xz0))
% Found (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7) as proof of (((Xp Xx) Xy0)->(((Xp Xx) Xz0)->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of ((Xp Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx) Xy0)->(((Xp Xx) Xz0)->P)))=> (((((and_rect ((Xp Xx) Xy0)) ((Xp Xx) Xz0)) P) x6) x5)) ((Xp Xx) Xz0)) (fun (x6:((Xp Xx) Xy0)) (x7:((Xp Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx) Xy0)) ((Xp Xx) Xz0))->((Xp Xx) Xz0))))
% Found x6:((Xp Xx0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x6) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xy0) Xz)->((Xp Xx0) Xz))
% Found (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6) as proof of (((Xp Xx0) Xz)->(((Xp Xy0) Xz)->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of ((Xp Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xx0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xx0) Xz)) (fun (x6:((Xp Xx0) Xz)) (x7:((Xp Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xz)) ((Xp Xy0) Xz))->((Xp Xx0) Xz))))
% Found x60:=(x6 x40):((Xp Xx) Xz0)
% Found (x6 x40) as proof of ((Xp Xx) Xz0)
% Found (fun (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)) as proof of (((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->((Xp Xx) Xz0))
% Found (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40))) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40))) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40))) as proof of ((Xp Xx) Xz0)
% Found (fun (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of ((Xp Xx) Xz0)
% Found (fun (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0)))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))->(((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))) P) x5) x4)) ((Xp Xx) Xz0)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0))) (x6:((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))=> (x6 x40)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0)))))
% Found x50:=(x5 x40):((Xp Xx0) Xz)
% Found (x5 x40) as proof of ((Xp Xx0) Xz)
% Found (fun (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->((Xp Xx0) Xz))
% Found (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)) as proof of (((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40))) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40))) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40))) as proof of ((Xp Xx0) Xz)
% Found (fun (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of ((Xp Xx0) Xz)
% Found (fun (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz)))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))) (x40:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))->(((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))) P) x5) x4)) ((Xp Xx0) Xz)) (fun (x5:((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) (x6:((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))=> (x5 x40)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz))) ((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz)))))
% Found x5:((Xp Xx00) Xy0)
% Found (fun (x6:((Xp Xy00) Xy0))=> x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect10 (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect1 ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x6:((Xp Xx0) Xz0)
% Found (fun (x6:((Xp Xx0) Xz0))=> x6) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect10 (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect1 ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x7:((Xr Xx) Xz0)
% Found (fun (x7:((Xr Xx) Xz0))=> x7) as proof of ((Xr Xx) Xz0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x6:((Xr Xx0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x6) as proof of ((Xr Xx0) Xz)
% Found (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found (fun (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x6:((Xr Xx0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x6) as proof of ((Xr Xx0) Xz)
% Found (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found (fun (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x7:((Xr Xx) Xz0)
% Found (fun (x7:((Xr Xx) Xz0))=> x7) as proof of ((Xr Xx) Xz0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x7:((Xr Xx) Xz0)
% Found (fun (x7:((Xr Xx) Xz0))=> x7) as proof of ((Xr Xx) Xz0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7) as proof of (((Xr Xx) Xz0)->((Xr Xx) Xz0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xz0)->((Xr Xx) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found ((and_rect2 ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7)) as proof of ((Xr Xx) Xz0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of ((Xr Xx) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xz0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xz0)) P) x6) x5)) ((Xr Xx) Xz0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx) Xy0)) ((Xr Xx) Xz0))->((Xr Xx) Xz0))))
% Found x6:((Xr Xx0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x6) as proof of ((Xr Xx0) Xz)
% Found (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6) as proof of (((Xr Xy0) Xz)->((Xr Xx0) Xz))
% Found (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6) as proof of (((Xr Xx0) Xz)->(((Xr Xy0) Xz)->((Xr Xx0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found ((and_rect2 ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6)) as proof of ((Xr Xx0) Xz)
% Found (fun (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of ((Xr Xx0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz)))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xx0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xx0) Xz)) (fun (x6:((Xr Xx0) Xz)) (x7:((Xr Xy0) Xz))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xz)) ((Xr Xy0) Xz))->((Xr Xx0) Xz))))
% Found x500:=(x50 x400):((Xp Xx) Xz0)
% Found (x50 x400) as proof of ((Xp Xx) Xz0)
% Found ((x5 x30) x400) as proof of ((Xp Xx) Xz0)
% Found (fun (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)) as proof of ((Xp Xx) Xz0)
% Found (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)) as proof of (((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->((Xp Xx) Xz0))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->((Xp Xx) Xz0)))
% Found (and_rect20 (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400))) as proof of ((Xp Xx) Xz0)
% Found ((and_rect2 ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400))) as proof of ((Xp Xx) Xz0)
% Found (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400))) as proof of ((Xp Xx) Xz0)
% Found (fun (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of ((Xp Xx) Xz0)
% Found (fun (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0))
% Found (fun (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0)))
% Found (fun (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (forall (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))->(((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0)))) P) x4) x3)) ((Xp Xx) Xz0)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xy0)))) (x5:((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))=> ((x5 x30) x400)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx) Xy0)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xx) Xz0))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx) Xz0))))))
% Found x401:=(x40 x400):((Xp Xx0) Xz)
% Found (x40 x400) as proof of ((Xp Xx0) Xz)
% Found ((x4 x30) x400) as proof of ((Xp Xx0) Xz)
% Found (fun (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)) as proof of ((Xp Xx0) Xz)
% Found (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->((Xp Xx0) Xz))
% Found (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)) as proof of (((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->((Xp Xx0) Xz)))
% Found (and_rect20 (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400))) as proof of ((Xp Xx0) Xz)
% Found ((and_rect2 ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400))) as proof of ((Xp Xx0) Xz)
% Found (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400))) as proof of ((Xp Xx0) Xz)
% Found (fun (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of ((Xp Xx0) Xz)
% Found (fun (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz))
% Found (fun (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of ((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz)))
% Found (fun (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (forall (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))) (x30:(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))) (x400:(forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00))))=> (((fun (P:Type) (x4:(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))->(((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))->P)))=> (((((and_rect ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz)))) P) x4) x3)) ((Xp Xx0) Xz)) (fun (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xz))))=> ((x4 x30) x400)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xz)))) ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx0:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx0) Xz00)))->((Xp Xy0) Xz))))->((forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))->((forall (Xx00:a) (Xy0:a) (Xz00:a), (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz))))))
% Found x50:=(x5 x30):((Xp Xx0) Xz0)
% Found (x5 x30) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect10 (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect1 ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x3:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x5:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x5 x30)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found x40:=(x4 x30):((Xp Xx00) Xy0)
% Found (x4 x30) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect10 (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect1 ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x3:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x5:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x4 x30)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x5 as proof of ((Xr Xy00) Xy0)
% Found (x100 x5) as proof of ((Xp Xy00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x1 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x1 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy00)
% Found (x100 x5) as proof of ((Xp Xx0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x1 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x1 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x3 as proof of ((Xr Xy00) Xy0)
% Found (x3000 x3) as proof of ((Xp Xy00) Xy0)
% Found ((x300 Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x30 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x30 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy00)
% Found (x3000 x3) as proof of ((Xp Xx0) Xy00)
% Found ((x300 Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x30 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x30 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x4 as proof of ((Xr Xy00) Xy0)
% Found (x300 x4) as proof of ((Xp Xy00) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x4) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x4) as proof of ((Xp Xy00) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x5 as proof of ((Xr Xy00) Xy0)
% Found (x300 x5) as proof of ((Xp Xy00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x4 as proof of ((Xr Xx0) Xy00)
% Found (x300 x4) as proof of ((Xp Xx0) Xy00)
% Found ((x30 Xy00) x4) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x4) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x4) as proof of ((Xp Xx0) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy00)
% Found (x300 x5) as proof of ((Xp Xx0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x5 as proof of ((Xr Xy00) Xy0)
% Found (x300 x5) as proof of ((Xp Xy00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy00)
% Found (x300 x5) as proof of ((Xp Xx0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x30:=(x3 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x3 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (x3 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x400:=(x40 x30):((Xp Xx00) Xy00)
% Found (x40 x30) as proof of ((Xp Xx00) Xy00)
% Found ((x4 Xy00) x30) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00))
% Found (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00)))
% Found (and_rect10 (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect1 ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x4 Xy00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))->(((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) (x7:((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz))) ((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xz)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7)) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) P) x6) x5)) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) (x7:((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx) Xy0)) ((Xp Xy0) Xz0)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x3 as proof of ((Xr Xy00) Xy0)
% Found (x400 x3) as proof of ((Xp Xy00) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x4 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x4 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy00)
% Found (x400 x3) as proof of ((Xp Xx0) Xy00)
% Found ((x40 Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x4 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x4 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x300:=(x30 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x30 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x300:=(x30 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x30 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x8:((Xp Xx0) Xz0)
% Found (fun (x8:((Xp Xx0) Xz0))=> x8) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy00) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x5:((Xp Xx00) Xy0)
% Found (fun (x6:((Xp Xy00) Xy0))=> x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((Xp Xx00) Xy0)) (x6:((Xp Xy00) Xy0))=> x5))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x6:((Xp Xx0) Xz0)
% Found (fun (x6:((Xp Xx0) Xz0))=> x6) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((Xp Xx0) Xy00)) (x6:((Xp Xx0) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy00) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x6:((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((Xp Xx00) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xx0) Xz0)
% Found (fun (x8:((Xp Xx0) Xz0))=> x8) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x7:((Xp Xx0) Xz0)
% Found (fun (x7:((Xp Xx0) Xz0))=> x7) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((Xp Xx0) Xy00)) (x7:((Xp Xx0) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy00) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xx0) Xz0)
% Found (fun (x8:((Xp Xx0) Xz0))=> x8) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x2010:=(x201 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x201 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x20 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x20 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x4010:=(x401 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x401 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x40 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x40 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x40 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x40 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x40 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x40 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x3 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x300:=(x30 Xx00):(forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))
% Found (x30 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found (x30 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found x500:=(x50 x30):((Xp Xx0) Xz0)
% Found (x50 x30) as proof of ((Xp Xx0) Xz0)
% Found ((x5 Xy00) x30) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect10 (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect1 ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))
% Found (fun (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x5 Xy00) x30)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))))
% Found x8:((Xp Xx0) Xz0)
% Found (fun (x8:((Xp Xx0) Xz0))=> x8) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy00) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found x2010:=(x201 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x201 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x20 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x20 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy00) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xy00) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xx0) Xz0)
% Found (fun (x8:((Xp Xx0) Xz0))=> x8) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xz0)->((Xp Xx0) Xz0))
% Found (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8) as proof of (((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xx0) Xy00)->(((Xp Xx0) Xz0)->P)))=> (((((and_rect ((Xp Xx0) Xy00)) ((Xp Xx0) Xz0)) P) x7) x6)) ((Xp Xx0) Xz0)) (fun (x7:((Xp Xx0) Xy00)) (x8:((Xp Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xz0))->((Xp Xx0) Xz0))))
% Found x70:=(x7 x50):((Xp Xx0) Xz0)
% Found (x7 x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found x60:=(x6 x50):((Xp Xx00) Xy0)
% Found (x6 x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x60:=(x6 x400):((Xp Xx0) Xz0)
% Found (x6 x400) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)))) as proof of (forall (Xz0:a), (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x6:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x6 x400)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found x50:=(x5 x400):((Xp Xx00) Xy0)
% Found (x5 x400) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x5 x400)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xy0)))))
% Found x70:=(x7 x40):((Xp Xx0) Xz0)
% Found (x7 x40) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x40:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x40:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x40:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x40:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)))) as proof of (forall (Xz0:a), (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x40:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x40:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x40)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found x70:=(x7 x50):((Xp Xx0) Xz0)
% Found (x7 x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found x60:=(x6 x50):((Xp Xx00) Xy0)
% Found (x6 x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found x60:=(x6 x40):((Xp Xx00) Xy0)
% Found (x6 x40) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x40:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x40:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x40:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x40:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x40:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x40:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x40)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xy0)))))
% Found x100:=(x10 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x10 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x1 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x1 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x100:=(x10 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x10 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x1 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x1 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found (fun (Xy01:a)=> ((x1 Xx00) Xy01)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x300:=(x30 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x30 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found (fun (Xy01:a)=> ((x3 Xx00) Xy01)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x3 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x300:=(x30 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x30 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found x3000:=(x300 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x300 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x30 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x30 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found (fun (Xy01:a)=> ((x30 Xx00) Xy01)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x3000:=(x300 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x300 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x30 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x30 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found x300:=(x30 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x30 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found (fun (Xy01:a)=> ((x3 Xx00) Xy01)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x300:=(x30 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x30 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found x70:=(x7 x50):((Xp Xx0) Xz0)
% Found (x7 x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found x60:=(x6 x50):((Xp Xx00) Xy0)
% Found (x6 x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found x40:=(x4 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x4 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found (x4 Xx00) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xy00) Xy0)))
% Found x300:=(x30 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x30 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found x300:=(x30 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x30 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x3 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found (fun (Xy01:a)=> ((x3 Xx00) Xy01)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x5000:=(x500 x30):((Xp Xx00) Xz0)
% Found (x500 x30) as proof of ((Xp Xx00) Xz0)
% Found ((x50 Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (((x5 Xx00) Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (fun (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0))
% Found (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0)))
% Found (and_rect10 (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect1 ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x5 Xx00) Xy00) x30)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x6:((Xr Xx0) Xz0)
% Found (fun (x6:((Xr Xx0) Xz0))=> x6) as proof of ((Xr Xx0) Xz0)
% Found (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x5:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x5) x4)) ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x4:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x5) x4)) ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x5) x4)) ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x5) x4)) ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x5) x4)) ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x5) x4)) ((Xr Xx0) Xz0)) (fun (x5:((Xr Xx0) Xy00)) (x6:((Xr Xx0) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x5:((Xr Xx00) Xy0)
% Found (fun (x6:((Xr Xy00) Xy0))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x5:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x5) x4)) ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x4:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x5) x4)) ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x4:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x5) x4)) ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x5) x4)) ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x5) x4)) ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x5) x4)) ((Xr Xx00) Xy0)) (fun (x5:((Xr Xx00) Xy0)) (x6:((Xr Xy00) Xy0))=> x5))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x6:((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xy00) Xy0))=> x6) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:((Xr Xx00) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x7:((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xz0))=> x7) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x5:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:((Xr Xx0) Xy00)) (x7:((Xr Xx0) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x70:=(x7 x50):((Xp Xx0) Xz0)
% Found (x7 x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of (((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x50:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x50:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x50:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x50:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) (x50:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))->(((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))) (x7:((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found x60:=(x6 x50):((Xp Xx00) Xy0)
% Found (x6 x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)) as proof of (((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x50:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x50:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x50:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x50:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) (x50:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x6:(((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))->(((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))) (x7:((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xy0))) ((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xy0)))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x60:=(x6 x30):((Xp Xx00) Xy0)
% Found (x6 x30) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xp Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0))) P) x6) x5)) ((Xp Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))=> (x6 x30)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xp Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found x70:=(x7 x30):((Xp Xx0) Xz0)
% Found (x7 x30) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)) as proof of ((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)))) as proof of (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)))) as proof of (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))) (x30:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xp Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xp Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))=> (x7 x30)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xp Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x400:=(x40 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x40 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x4 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found ((x4 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xx00) Xy00))
% Found x400:=(x40 Xy01):(((Xr Xx00) Xy01)->((Xp Xx00) Xy01))
% Found (x40 Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x4 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found ((x4 Xx00) Xy01) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found (fun (Xy01:a)=> ((x4 Xx00) Xy01)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x600:=(x60 x50):((Xp Xx00) Xy00)
% Found (x60 x50) as proof of ((Xp Xx00) Xy00)
% Found ((x6 Xy00) x50) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found x600:=(x60 x50):((Xp Xx00) Xy00)
% Found (x60 x50) as proof of ((Xp Xx00) Xy00)
% Found ((x6 Xy00) x50) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found x600:=(x60 x400):((Xp Xx0) Xz0)
% Found (x60 x400) as proof of ((Xp Xx0) Xz0)
% Found ((x6 x30) x400) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x30:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x30:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x30:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x30:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of (forall (Xz0:a), (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x30:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x30:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x30) x400)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found x500:=(x50 x400):((Xp Xx00) Xy0)
% Found (x50 x400) as proof of ((Xp Xx00) Xy0)
% Found ((x5 x40) x400) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((Xp Xx00) Xy0))
% Found (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x400)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found x500:=(x50 x400):((Xp Xx00) Xy0)
% Found (x50 x400) as proof of ((Xp Xx00) Xy0)
% Found ((x5 x30) x400) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((Xp Xx00) Xy0))
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x30:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x30:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x30:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x30:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x30:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x30:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x30) x400)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xy0)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xy0))))))
% Found x600:=(x60 x400):((Xp Xx0) Xz0)
% Found (x60 x400) as proof of ((Xp Xx0) Xz0)
% Found ((x6 x40) x400) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:((Xr Xx0) Xy0)) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x400)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x4000:=(x400 x30):((Xp Xx0) Xy00)
% Found (x400 x30) as proof of ((Xp Xx0) Xy00)
% Found ((x40 Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00))
% Found (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00)))
% Found (and_rect10 (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect1 ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx0) Xy0)
% Found x600:=(x60 x50):((Xp Xx00) Xy00)
% Found (x60 x50) as proof of ((Xp Xx00) Xy00)
% Found ((x6 Xy00) x50) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy00) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xy00) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy00) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xx0) Xz0)
% Found (fun (x8:((Xr Xx0) Xz0))=> x8) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xz0)->((Xr Xx0) Xz0))
% Found (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8) as proof of (((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x6:((and ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xx0) Xy00)->(((Xr Xx0) Xz0)->P)))=> (((((and_rect ((Xr Xx0) Xy00)) ((Xr Xx0) Xz0)) P) x7) x6)) ((Xr Xx0) Xz0)) (fun (x7:((Xr Xx0) Xy00)) (x8:((Xr Xx0) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xx0) Xy0)) ((Xr Xx0) Xz0))->((Xr Xx0) Xz0))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx0) Xy0)
% Found x2010:=(x201 Xy0):(((and ((Xp Xx) Xy0)) ((Xp Xy0) Xy0))->((Xp Xx) Xy0))
% Found (x201 Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x20 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found ((x20 Xy0) Xy0) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a)=> ((x20 Xy0) Xy0)) as proof of (a->(a->(a->(((and ((Xp Xx) Xy0)) ((Xp Xx) Xy0))->((Xp Xx) Xy0)))))
% Found x60:=(x6 x50):((Xr Xx00) Xy0)
% Found (x6 x50) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found x70:=(x7 x50):((Xr Xx0) Xz0)
% Found (x7 x50) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found x60:=(x6 x50):((Xr Xx00) Xy0)
% Found (x6 x50) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found x70:=(x7 x50):((Xr Xx0) Xz0)
% Found (x7 x50) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found x501:=(x50 x500):((Xp Xx00) Xy0)
% Found (x50 x500) as proof of ((Xp Xx00) Xy0)
% Found ((x5 x40) x500) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((Xp Xx00) Xy0))
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x40:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x40:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x40:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x40:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x40:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of (forall (Xy00:a), (a->(((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) (x40:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x500:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))->(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))) P) x5) x4)) ((Xp Xx00) Xy0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))) (x6:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))=> ((x5 x40) x500)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx00) Xz0)))->((Xp Xx0) Xy0)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xy0))))))
% Found x600:=(x60 x500):((Xp Xx0) Xz0)
% Found (x60 x500) as proof of ((Xp Xx0) Xz0)
% Found ((x6 x40) x500) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)) as proof of (((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)) as proof of (((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x40:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of (forall (Xz0:a), (((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x4:((and ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) (x40:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x500:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:(((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))->(((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))->P)))=> (((((and_rect ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))=> ((x6 x40) x500)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz0:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))) ((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy00)))->((forall (Xx00:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found x600:=(x60 x30):((Xp Xx00) Xy00)
% Found (x60 x30) as proof of ((Xp Xx00) Xy00)
% Found ((x6 Xy00) x30) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))=> ((x6 Xy00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx00) Xy0))))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> x6) as proof of (((Xr Xx00) Xy01)->((Xr Xy00) Xy01))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xx00) Xy00)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> x6) as proof of (((Xr Xx00) Xy01)->((Xr Xy00) Xy01))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xx00) Xy00)
% Found x4:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found (fun (x4:((Xr Xx00) Xy01))=> x4) as proof of ((Xr Xy00) Xy01)
% Found (fun (Xy01:a) (x4:((Xr Xx00) Xy01))=> x4) as proof of (((Xr Xx00) Xy01)->((Xr Xy00) Xy01))
% Found x4:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found (fun (x4:((Xr Xx00) Xy01))=> x4) as proof of ((Xr Xx00) Xy00)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found (fun (x5:((Xr Xx00) Xy01))=> x5) as proof of ((Xr Xy00) Xy01)
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01))=> x5) as proof of (((Xr Xx00) Xy01)->((Xr Xy00) Xy01))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found (fun (x5:((Xr Xx00) Xy01))=> x5) as proof of ((Xr Xx00) Xy00)
% Found x60:=(x6 x50):((Xr Xx00) Xy0)
% Found (x6 x50) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->((Xr Xx00) Xy0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50))) as proof of ((Xr Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx00) Xy0))->((((Xr Xx0) Xy0)->((Xr Xy00) Xy0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0))) P) x6) x5)) ((Xr Xx00) Xy0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (x7:(((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))) (((Xr Xx0) Xy0)->((Xr Xy00) Xy0)))->(((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found x70:=(x7 x50):((Xr Xx0) Xz0)
% Found (x7 x50) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->((Xr Xx0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)) as proof of ((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))) (x50:((Xr Xx0) Xy0))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy0)->((Xr Xx0) Xy00))->((((Xr Xx0) Xy0)->((Xr Xx0) Xz0))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (x7:(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))=> (x7 x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((Xr Xx0) Xy00))) (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))->(((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found x5000:=(x500 x40):((Xp Xx00) Xy00)
% Found (x500 x40) as proof of ((Xp Xx00) Xy00)
% Found ((x50 Xy00) x40) as proof of ((Xp Xx00) Xy00)
% Found (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))->((Xp Xx00) Xy00))
% Found (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy00))
% Found (fun (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy00)))
% Found (fun (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000))))) (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x5 Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))))
% Found x4010:=(x401 x400):((Xp Xx00) Xy0)
% Found (x401 x400) as proof of ((Xp Xx00) Xy0)
% Found ((x40 x300) x400) as proof of ((Xp Xx00) Xy0)
% Found (((x4 x30) x300) x400) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((Xp Xx00) Xy0))
% Found (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400))) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400))) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of ((Xp Xx00) Xy0)
% Found (fun (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))
% Found (fun (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))
% Found (fun (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))
% Found (fun (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of (forall (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0))))) P) x4) x3)) ((Xp Xx00) Xy0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy00) Xy0)))))=> (((x4 x30) x300) x400)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy00) Xy0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))))
% Found x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))
% Found x300 as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))
% Found x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))
% Found x400 as proof of (forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))
% Found x30:((Xr Xx0) Xy0)
% Found x30 as proof of ((Xr Xx0) Xy0)
% Found (((x5 x30) x300) x400) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((Xp Xx0) Xz0))
% Found (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)) as proof of ((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of ((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x3:((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (x30:((Xr Xx0) Xy0)) (x300:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))) (x400:(forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))) (x5:(((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((x5 x30) x300) x400)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (((Xr Xx0) Xy0)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x3 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x3 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> (((x3 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x100 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x10 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xx0:a
% Found x50 as proof of ((Xr Xy01) Xy00)
% Found (x100 x50) as proof of ((Xp Xy01) Xy00)
% Found ((x10 Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x100 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x6 as proof of ((Xr Xx00) Xy01)
% Found (x100 x6) as proof of ((Xp Xx00) Xy01)
% Found ((x10 Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x6 as proof of ((Xr Xy01) Xy00)
% Found (x100 x6) as proof of ((Xp Xy01) Xy00)
% Found ((x10 Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x100 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x10 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x100 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x10 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x50:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x50 as proof of ((Xr Xy01) Xy0)
% Found (x100 x50) as proof of ((Xp Xy01) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy00)
% Found (x100 x5) as proof of ((Xp Xy01) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found x50:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x50 as proof of ((Xr Xx0) Xy01)
% Found (x100 x50) as proof of ((Xp Xx0) Xy01)
% Found ((x10 Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> x6) as proof of (((Xr Xx00) Xy01)->((Xr Xy00) Xy01))
% Found x3:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x3 as proof of ((Xr Xy000) Xy00)
% Found (x30000 x3) as proof of ((Xp Xy000) Xy00)
% Found ((x3000 Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found (((x300 Xy000) Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found (((x300 Xy000) Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found x30:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x30 as proof of ((Xr Xx0) Xy000)
% Found (x30000 x30) as proof of ((Xp Xx0) Xy000)
% Found ((x3000 Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x300 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x300 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xx00) Xy00)
% Found x3:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x3 as proof of ((Xr Xx00) Xy000)
% Found (x30000 x3) as proof of ((Xp Xx00) Xy000)
% Found ((x3000 Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found (((x300 Xx00) Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found (((x300 Xx00) Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found x30:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x30 as proof of ((Xr Xy000) Xy0)
% Found (x30000 x30) as proof of ((Xp Xy000) Xy0)
% Found ((x3000 Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found (((x300 Xy000) Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found (((x300 Xy000) Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x300 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xx0:a
% Found x50 as proof of ((Xr Xy01) Xy00)
% Found (x300 x50) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x6 as proof of ((Xr Xx00) Xy01)
% Found (x300 x6) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x4 as proof of ((Xr Xy000) Xy00)
% Found (x3000 x4) as proof of ((Xp Xy000) Xy00)
% Found ((x300 Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x3000 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x300 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x6 as proof of ((Xr Xy01) Xy00)
% Found (x300 x6) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x300 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x3000 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x300 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x30 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x30 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x3000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x300 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x3000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x300 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x3000 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x300 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x30 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x30 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x4 as proof of ((Xr Xy000) Xy00)
% Found (x300 x4) as proof of ((Xp Xy000) Xy00)
% Found ((x30 Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found x40:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x40 as proof of ((Xr Xx0) Xy000)
% Found (x300 x40) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x40) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x40) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x40) as proof of ((Xp Xx0) Xy000)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x4 as proof of ((Xr Xy000) Xy00)
% Found (x3000 x4) as proof of ((Xp Xy000) Xy00)
% Found ((x300 Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x3000 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x300 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x4 as proof of ((Xr Xy000) Xy00)
% Found (x3000 x4) as proof of ((Xp Xy000) Xy00)
% Found ((x300 Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x3000 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x300 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x40:((Xr Xx0) Xy00)
% Instantiate: Xy000:=Xx0:a
% Found x40 as proof of ((Xr Xy000) Xy00)
% Found (x300 x40) as proof of ((Xp Xy000) Xy00)
% Found ((x30 Xy00) x40) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x40) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x40) as proof of ((Xp Xy000) Xy00)
% Found x4:((Xr Xx00) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x300 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x30 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x300 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x50:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x50 as proof of ((Xr Xy01) Xy0)
% Found (x300 x50) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x300 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x30 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x40:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x40 as proof of ((Xr Xy000) Xy0)
% Found (x300 x40) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x40) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x40) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x40) as proof of ((Xp Xy000) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x5 as proof of ((Xr Xy000) Xy00)
% Found (x300 x5) as proof of ((Xp Xy000) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x4 as proof of ((Xr Xx0) Xy000)
% Found (x300 x4) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x4 as proof of ((Xr Xy000) Xy0)
% Found (x300 x4) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy000)
% Found (x300 x5) as proof of ((Xp Xx00) Xy000)
% Found ((x30 Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x5 as proof of ((Xr Xy000) Xy00)
% Found (x300 x5) as proof of ((Xp Xy000) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x4 as proof of ((Xr Xx0) Xy000)
% Found (x300 x4) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x3000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x300 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x3000 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x300 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x30 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x30 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy00)
% Found (x300 x5) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found x50:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x50 as proof of ((Xr Xx0) Xy01)
% Found (x300 x50) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy000)
% Found (x300 x5) as proof of ((Xp Xx00) Xy000)
% Found ((x30 Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x4 as proof of ((Xr Xy000) Xy0)
% Found (x300 x4) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x300 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xx0:a
% Found x50 as proof of ((Xr Xy01) Xy00)
% Found (x300 x50) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x6 as proof of ((Xr Xx00) Xy01)
% Found (x300 x6) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x6) as proof of ((Xp Xx00) Xy01)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x6 as proof of ((Xr Xy01) Xy00)
% Found (x300 x6) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x300 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy00)
% Found (x300 x5) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found x50:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x50 as proof of ((Xr Xx0) Xy01)
% Found (x300 x50) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found x50:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x50 as proof of ((Xr Xy01) Xy0)
% Found (x300 x50) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x50) as proof of ((Xp Xy01) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x300 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x700:=(x70 x50):((Xp Xx0) Xz0)
% Found (x70 x50) as proof of ((Xp Xx0) Xz0)
% Found ((x7 Xy00) x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))))
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x100 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x50 as proof of ((Xr Xx0) Xy01)
% Found (x100 x50) as proof of ((Xp Xx0) Xy01)
% Found ((x10 Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x100 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x10 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x1 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x1 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x5 as proof of ((Xr Xy00) Xy0)
% Found (x100 x5) as proof of ((Xp Xy00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x1 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x1 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x100 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x10 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x1 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x1 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy00)
% Found (x100 x5) as proof of ((Xp Xx0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x1 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x1 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found x700:=(x70 x50):((Xp Xx0) Xz0)
% Found (x70 x50) as proof of ((Xp Xx0) Xz0)
% Found ((x7 Xy00) x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))))
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x50 as proof of ((Xr Xx0) Xy01)
% Found (x300 x50) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x100 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of (((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x100 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x5:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x5) x4)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x4:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x5) x4)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5))) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x4:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x5) x4)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5))) as proof of (((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x5) x4)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5))) as proof of (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x5) x4)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x5) x4)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x6:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x5))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x4:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x4 as proof of ((Xr Xx00) Xy00)
% Found (x3000 x4) as proof of ((Xp Xx00) Xy00)
% Found ((x300 Xy00) x4) as proof of ((Xp Xx00) Xy00)
% Found (((x30 Xx00) Xy00) x4) as proof of ((Xp Xx00) Xy00)
% Found (((x30 Xx00) Xy00) x4) as proof of ((Xp Xx00) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x3 as proof of ((Xr Xy00) Xy0)
% Found (x3000 x3) as proof of ((Xp Xy00) Xy0)
% Found ((x300 Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x30 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x30 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x300 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x30 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x5 as proof of ((Xr Xy00) Xy0)
% Found (x300 x5) as proof of ((Xp Xy00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x5:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x5) x4)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x4:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x5) x4)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x4:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x5) x4)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x5) x4)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x5) x4)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x5:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x5) x4)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x5:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))))
% Found x4:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x4 as proof of ((Xr Xy00) Xy01)
% Found (x3000 x4) as proof of ((Xp Xy00) Xy01)
% Found ((x300 Xy01) x4) as proof of ((Xp Xy00) Xy01)
% Found (((x30 Xy00) Xy01) x4) as proof of ((Xp Xy00) Xy01)
% Found (((x30 Xy00) Xy01) x4) as proof of ((Xp Xy00) Xy01)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy00)
% Found (x3000 x3) as proof of ((Xp Xx0) Xy00)
% Found ((x300 Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x30 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x30 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x5:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x6) x5)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x7:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x6))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x5 as proof of ((Xr Xx00) Xy00)
% Found (x300 x5) as proof of ((Xp Xx00) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x5) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x5) as proof of ((Xp Xx00) Xy00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x4 as proof of ((Xr Xy00) Xy0)
% Found (x300 x4) as proof of ((Xp Xy00) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x4) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x4) as proof of ((Xp Xy00) Xy0)
% Found x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x6:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x6) x5)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x6:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x5 as proof of ((Xr Xy00) Xy01)
% Found (x300 x5) as proof of ((Xp Xy00) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x5) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x5) as proof of ((Xp Xy00) Xy01)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x4 as proof of ((Xr Xx0) Xy00)
% Found (x300 x4) as proof of ((Xp Xx0) Xy00)
% Found ((x30 Xy00) x4) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x4) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x4) as proof of ((Xp Xx0) Xy00)
% Found x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x300 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x30 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy00)
% Found (x300 x5) as proof of ((Xp Xx0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x300 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of (((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x300 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x700:=(x70 x50):((Xp Xx0) Xz0)
% Found (x70 x50) as proof of ((Xp Xx0) Xz0)
% Found ((x7 Xy00) x50) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))))
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x50 as proof of ((Xr Xx0) Xy01)
% Found (x300 x50) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x50) as proof of ((Xp Xx0) Xy01)
% Found x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x300 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x30 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x5 as proof of ((Xr Xy00) Xy0)
% Found (x300 x5) as proof of ((Xp Xy00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found (((x3 Xy00) Xy0) x5) as proof of ((Xp Xy00) Xy0)
% Found x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x300 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x30 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy00)
% Found (x300 x5) as proof of ((Xp Xx0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found (((x3 Xx0) Xy00) x5) as proof of ((Xp Xx0) Xy00)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> x6) as proof of (((Xr Xx00) Xy01)->((Xr Xy00) Xy01))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found (fun (x6:((Xr Xx00) Xy01))=> x6) as proof of ((Xr Xx00) Xy00)
% Found x600:=(x60 x50):((Xr Xx00) Xy00)
% Found (x60 x50) as proof of ((Xr Xx00) Xy00)
% Found ((x6 Xy00) x50) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))))
% Found x600:=(x60 x50):((Xr Xx00) Xy00)
% Found (x60 x50) as proof of ((Xr Xx00) Xy00)
% Found ((x6 Xy00) x50) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))))
% Found x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))->(((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x7:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (x8:((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x100 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of (((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (forall (Xy000:a), (a->(((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))->(((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))) P) x7) x6)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x7:((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (x8:((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))=> x7))) as proof of (forall (Xx0:a) (Xy000:a), (a->(((and ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))) ((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x100 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x100 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x10 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x1 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x1 Xx00) Xy00) x6)) as proof of ((Xp Xx00) Xy00)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x100 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x6)) as proof of ((Xp Xx00) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x100 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x100 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x10 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x1 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x1 Xy00) Xy01) x6)) as proof of ((Xp Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy00) Xy01) x6)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x300 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x30 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x3 Xx00) Xy00) x6)) as proof of ((Xp Xx00) Xy00)
% Found x4:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x4 as proof of ((Xr Xx00) Xy00)
% Found (x3000 x4) as proof of ((Xp Xx00) Xy00)
% Found ((x300 Xy00) x4) as proof of ((Xp Xx00) Xy00)
% Found (((x30 Xx00) Xy00) x4) as proof of ((Xp Xx00) Xy00)
% Found (fun (x4:((Xr Xx00) Xy01))=> (((x30 Xx00) Xy00) x4)) as proof of ((Xp Xx00) Xy00)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x5 as proof of ((Xr Xx00) Xy00)
% Found (x300 x5) as proof of ((Xp Xx00) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x5) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:((Xr Xx00) Xy01))=> (((x3 Xx00) Xy00) x5)) as proof of ((Xp Xx00) Xy00)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x5 as proof of ((Xr Xy00) Xy01)
% Found (x300 x5) as proof of ((Xp Xy00) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x5) as proof of ((Xp Xy00) Xy01)
% Found (fun (x5:((Xr Xx00) Xy01))=> (((x3 Xy00) Xy01) x5)) as proof of ((Xp Xy00) Xy01)
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01))=> (((x3 Xy00) Xy01) x5)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x4:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x4 as proof of ((Xr Xy00) Xy01)
% Found (x3000 x4) as proof of ((Xp Xy00) Xy01)
% Found ((x300 Xy01) x4) as proof of ((Xp Xy00) Xy01)
% Found (((x30 Xy00) Xy01) x4) as proof of ((Xp Xy00) Xy01)
% Found (fun (x4:((Xr Xx00) Xy01))=> (((x30 Xy00) Xy01) x4)) as proof of ((Xp Xy00) Xy01)
% Found (fun (Xy01:a) (x4:((Xr Xx00) Xy01))=> (((x30 Xy00) Xy01) x4)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x300 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x3 Xx00) Xy0) x6)) as proof of ((Xp Xx00) Xy0)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x300 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x30 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x3 Xy00) Xy01) x6)) as proof of ((Xp Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy00) Xy01) x6)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x4 as proof of ((Xr Xy000) Xy00)
% Found (x4000 x4) as proof of ((Xp Xy000) Xy00)
% Found ((x400 Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x40 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x40 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x4000 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x400 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x40 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x40 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x300 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x6)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x6)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x6 as proof of ((Xr Xy01) Xy00)
% Found (x400 x6) as proof of ((Xp Xy01) Xy00)
% Found ((x40 Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy01)
% Found (x400 x3) as proof of ((Xp Xx0) Xy01)
% Found ((x40 Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x4000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x400 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x40 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x40 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x4000 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x400 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x40 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x40 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x400 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x6 as proof of ((Xr Xx00) Xy000)
% Found (x400 x6) as proof of ((Xp Xx00) Xy000)
% Found ((x40 Xy000) x6) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x6) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x6) as proof of ((Xp Xx00) Xy000)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x5 as proof of ((Xr Xy000) Xy00)
% Found (x400 x5) as proof of ((Xp Xy000) Xy00)
% Found ((x40 Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x4 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x4 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x400 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x40 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x4 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x4 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy000)
% Found (x400 x5) as proof of ((Xp Xx00) Xy000)
% Found ((x40 Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x400 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx00) Xy01)
% Found (x310 x5) as proof of ((Xp Xx00) Xy01)
% Found ((x31 Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x5) as proof of ((Xp Xx00) Xy01)
% Found x30:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xx0:a
% Found x30 as proof of ((Xr Xy01) Xy00)
% Found (x310 x30) as proof of ((Xp Xy01) Xy00)
% Found ((x31 Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found x600:=(x60 x50):((Xr Xx00) Xy00)
% Found (x60 x50) as proof of ((Xr Xx00) Xy00)
% Found ((x6 Xy00) x50) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx00) Xy00))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50))) as proof of ((Xr Xx00) Xy00)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy000)))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))=> ((x6 Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx00) Xy00)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx00) Xy0))))))
% Found x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))
% Found x400 as proof of (forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))
% Found x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))
% Found x300 as proof of (forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))
% Found x30:((Xr Xx0) Xy00)
% Found x30 as proof of ((Xr Xx0) Xy00)
% Found (((x40 x30) x300) x400) as proof of ((Xp Xx00) Xy00)
% Found ((((x4 Xy00) x30) x300) x400) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))->((Xp Xx00) Xy00))
% Found (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400))) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400))) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of ((Xp Xx00) Xy00)
% Found (fun (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy00))
% Found (fun (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy00)))
% Found (fun (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy00))))
% Found (fun (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))
% Found (fun (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx00) Xy00)) (fun (x4:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy000)))))) (x5:(forall (Xy000:a), (((Xr Xx0) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> ((((x4 Xy00) x30) x300) x400)))) as proof of (forall (Xx00:a) (Xy0:a), (a->(((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy00)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))))))
% Found x30:((Xr Xx0) Xy00)
% Instantiate: Xy000:=Xx0:a
% Found x30 as proof of ((Xr Xy000) Xy00)
% Found (x30000 x30) as proof of ((Xp Xy000) Xy00)
% Found ((x3000 Xy00) x30) as proof of ((Xp Xy000) Xy00)
% Found (((x300 Xy000) Xy00) x30) as proof of ((Xp Xy000) Xy00)
% Found (((x300 Xy000) Xy00) x30) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx00) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx00) Xy000)
% Found (x30000 x3) as proof of ((Xp Xx00) Xy000)
% Found ((x3000 Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found (((x300 Xx00) Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found (((x300 Xx00) Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x5 as proof of ((Xr Xy000) Xy00)
% Found (x310 x5) as proof of ((Xp Xy000) Xy00)
% Found ((x31 Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x5) as proof of ((Xp Xy000) Xy00)
% Found x30:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x30 as proof of ((Xr Xx0) Xy000)
% Found (x310 x30) as proof of ((Xp Xx0) Xy000)
% Found ((x31 Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x300 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x30 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x3 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x3 Xx00) Xy00) x6)) as proof of ((Xp Xx00) Xy00)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy000)
% Found (x310 x5) as proof of ((Xp Xx00) Xy000)
% Found ((x31 Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x5) as proof of ((Xp Xx00) Xy000)
% Found x30:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x30 as proof of ((Xr Xy000) Xy0)
% Found (x310 x30) as proof of ((Xp Xy000) Xy0)
% Found ((x31 Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x300 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x30 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x3 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x3 Xy00) Xy01) x6)) as proof of ((Xp Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy00) Xy01) x6)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x6 as proof of ((Xr Xy01) Xy00)
% Found (x400 x6) as proof of ((Xp Xy01) Xy00)
% Found ((x40 Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x6) as proof of ((Xp Xy01) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy01)
% Found (x400 x3) as proof of ((Xp Xx0) Xy01)
% Found ((x40 Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x400 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x6:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x6 as proof of ((Xr Xx00) Xy000)
% Found (x400 x6) as proof of ((Xp Xx00) Xy000)
% Found ((x40 Xy000) x6) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x6) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x6) as proof of ((Xp Xx00) Xy000)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7)) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xy01:a), (a->(((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))->(((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))->P)))=> (((((and_rect ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0))) P) x7) x6)) ((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (fun (x7:((and ((Xp Xx00) Xy00)) ((Xp Xy00) Xy0))) (x8:((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))=> x7))) as proof of (forall (Xx0:a) (Xy01:a), (a->(((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xy01) Xy00)) ((Xp Xy00) Xy0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x400 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x40 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x4 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x4 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xx0:a
% Found x3 as proof of ((Xr Xy00) Xy0)
% Found (x400 x3) as proof of ((Xp Xy00) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x4 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found (((x4 Xy00) Xy0) x3) as proof of ((Xp Xy00) Xy0)
% Found x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8) as proof of (((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (and_rect20 (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8)) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))
% Found (fun (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))))=> (((fun (P:Type) (x7:(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))->(((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))->P)))=> (((((and_rect ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) P) x7) x6)) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0))) (fun (x7:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy01))) (x8:((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xy0))) ((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))->((and ((Xp Xx0) Xy00)) ((Xp Xy00) Xz0)))))
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x400 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x40 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x4 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x4 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy00)
% Found (x400 x3) as proof of ((Xp Xx0) Xy00)
% Found ((x40 Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x4 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found (((x4 Xx0) Xy00) x3) as proof of ((Xp Xx0) Xy00)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx0) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x100 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x6)) as proof of ((Xp Xx00) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x100 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x700:=(x70 x30):((Xp Xx0) Xz0)
% Found (x70 x30) as proof of ((Xp Xx0) Xz0)
% Found ((x7 Xy00) x30) as proof of ((Xp Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xy00:a) (x30:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> ((x7 Xy00) x30)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xz0))))))
% Found x5:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xx00:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x310 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x31 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x30:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x30 as proof of ((Xr Xx0) Xy01)
% Found (x310 x30) as proof of ((Xp Xx0) Xy01)
% Found ((x31 Xy01) x30) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x30) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x30) as proof of ((Xp Xx0) Xy01)
% Found x7000:=(x700 x50):((Xp Xx00) Xz0)
% Found (x700 x50) as proof of ((Xp Xx00) Xz0)
% Found ((x70 Xy00) x50) as proof of ((Xp Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x50) as proof of ((Xp Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect2 ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x100 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x50:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x50 as proof of ((Xr Xx00) Xy01)
% Found (x100 x50) as proof of ((Xp Xx00) Xy01)
% Found ((x10 Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found (((x1 Xx00) Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found x7000:=(x700 x50):((Xp Xx00) Xz0)
% Found (x700 x50) as proof of ((Xp Xx00) Xz0)
% Found ((x70 Xy00) x50) as proof of ((Xp Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x50) as proof of ((Xp Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect2 ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x50:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x50 as proof of ((Xr Xx00) Xy01)
% Found (x300 x50) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found x6000:=(x600 x40):((Xp Xx0) Xz0)
% Found (x600 x40) as proof of ((Xp Xx0) Xz0)
% Found ((x60 Xy00) x40) as proof of ((Xp Xx0) Xz0)
% Found (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40) as proof of ((Xp Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((Xp Xx0) Xz0))
% Found (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xy00:a) (x40:((Xr Xx0) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx0) Xz0)) (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))) (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx0) Xy000))=> (((x6 Xy000) x401) x400)) Xy00) x40)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))))
% Found x4:((Xr Xx00) Xy0)
% Instantiate: Xy000:=Xx00:a
% Found x4 as proof of ((Xr Xy000) Xy0)
% Found (x300 x4) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found x40:((Xr Xx0) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x40 as proof of ((Xr Xx0) Xy000)
% Found (x300 x40) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x40) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x40) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x40) as proof of ((Xp Xx0) Xy000)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x5:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx0) Xy0)
% Found x70:=(x7 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (x7 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (forall (Xy01:a) (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (a->(forall (Xy01:a) (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy01)
% Found (x100 x5) as proof of ((Xp Xy0) Xy01)
% Found ((x10 Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (((x1 Xy0) Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (((x1 Xy0) Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found x60:=(x6 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (x6 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (forall (Xy01:a), (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy01:a), (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x50 as proof of ((Xr Xy0) Xy00)
% Found (x100 x50) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found x60:=(x6 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (x6 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (forall (Xy01:a), (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy01:a), (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy01) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x300 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x50 as proof of ((Xr Xy0) Xy00)
% Found (x300 x50) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found x70:=(x7 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (x7 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (forall (Xy01:a) (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (a->(forall (Xy01:a) (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy01)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x300 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy01)
% Found (x300 x5) as proof of ((Xp Xy0) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (((x3 Xy0) Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (((x3 Xy0) Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xy01:a
% Found x6 as proof of ((Xr Xx00) Xy00)
% Found (x400 x6) as proof of ((Xp Xx00) Xy00)
% Found ((x40 Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (((x4 Xx00) Xy00) x6) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x4 Xx00) Xy00) x6)) as proof of ((Xp Xx00) Xy00)
% Found x7000:=(x700 x50):((Xp Xx00) Xz0)
% Found (x700 x50) as proof of ((Xp Xx00) Xz0)
% Found ((x70 Xy00) x50) as proof of ((Xp Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x50) as proof of ((Xp Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect2 ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x50:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x50 as proof of ((Xr Xx00) Xy01)
% Found (x300 x50) as proof of ((Xp Xx00) Xy01)
% Found ((x30 Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x50) as proof of ((Xp Xx00) Xy01)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x400 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x30:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x30 as proof of ((Xr Xx00) Xy000)
% Found (x400 x30) as proof of ((Xp Xx00) Xy000)
% Found ((x40 Xy000) x30) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x30) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x30) as proof of ((Xp Xx00) Xy000)
% Found x6:((Xr Xx00) Xy01)
% Instantiate: Xy00:=Xx00:a
% Found x6 as proof of ((Xr Xy00) Xy01)
% Found (x400 x6) as proof of ((Xp Xy00) Xy01)
% Found ((x40 Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (((x4 Xy00) Xy01) x6) as proof of ((Xp Xy00) Xy01)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x4 Xy00) Xy01) x6)) as proof of ((Xp Xy00) Xy01)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x4 Xy00) Xy01) x6)) as proof of (((Xr Xx00) Xy01)->((Xp Xy00) Xy01))
% Found x30:((Xr Xx0) Xy00)
% Instantiate: Xy01:=Xx0:a
% Found x30 as proof of ((Xr Xy01) Xy00)
% Found (x400 x30) as proof of ((Xp Xy01) Xy00)
% Found ((x40 Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found x3:((Xr Xx00) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x3 as proof of ((Xr Xx00) Xy01)
% Found (x400 x3) as proof of ((Xp Xx00) Xy01)
% Found ((x40 Xy01) x3) as proof of ((Xp Xx00) Xy01)
% Found (((x4 Xx00) Xy01) x3) as proof of ((Xp Xx00) Xy01)
% Found (((x4 Xx00) Xy01) x3) as proof of ((Xp Xx00) Xy01)
% Found x3:((Xr Xx00) Xy0)
% Instantiate: Xy000:=Xx00:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x400 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x30:((Xr Xx0) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x30 as proof of ((Xr Xx0) Xy000)
% Found (x400 x30) as proof of ((Xp Xx0) Xy000)
% Found ((x40 Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x4 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x4 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy01)
% Found (x400 x3) as proof of ((Xp Xx0) Xy01)
% Found ((x40 Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found x30:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x30 as proof of ((Xr Xy01) Xy00)
% Found (x400 x30) as proof of ((Xp Xy01) Xy00)
% Found ((x40 Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x500 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x50 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x5 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x5 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x4 as proof of ((Xr Xx00) Xy000)
% Found (x500 x4) as proof of ((Xp Xx00) Xy000)
% Found ((x50 Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x5 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found (((x5 Xx00) Xy000) x4) as proof of ((Xp Xx00) Xy000)
% Found x4:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x4 as proof of ((Xr Xy01) Xy00)
% Found (x500 x4) as proof of ((Xp Xy01) Xy00)
% Found ((x50 Xy00) x4) as proof of ((Xp Xy01) Xy00)
% Found (((x5 Xy01) Xy00) x4) as proof of ((Xp Xy01) Xy00)
% Found (((x5 Xy01) Xy00) x4) as proof of ((Xp Xy01) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy01)
% Found (x500 x3) as proof of ((Xp Xx0) Xy01)
% Found ((x50 Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x5 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found (((x5 Xx0) Xy01) x3) as proof of ((Xp Xx0) Xy01)
% Found x3:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x3 as proof of ((Xr Xy01) Xy00)
% Found (x400 x3) as proof of ((Xp Xy01) Xy00)
% Found ((x40 Xy00) x3) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x3) as proof of ((Xp Xy01) Xy00)
% Found (((x4 Xy01) Xy00) x3) as proof of ((Xp Xy01) Xy00)
% Found x30:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x30 as proof of ((Xr Xx0) Xy01)
% Found (x400 x30) as proof of ((Xp Xx0) Xy01)
% Found ((x40 Xy01) x30) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x30) as proof of ((Xp Xx0) Xy01)
% Found (((x4 Xx0) Xy01) x30) as proof of ((Xp Xx0) Xy01)
% Found x3:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x3 as proof of ((Xr Xx00) Xy000)
% Found (x400 x3) as proof of ((Xp Xx00) Xy000)
% Found ((x40 Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found (((x4 Xx00) Xy000) x3) as proof of ((Xp Xx00) Xy000)
% Found x30:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x30 as proof of ((Xr Xy000) Xy0)
% Found (x400 x30) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x30) as proof of ((Xp Xy000) Xy0)
% Found x70:=(x7 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (x7 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (forall (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (forall (Xy000:a) (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))->((((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))=> (x7 x50)))) as proof of (a->(forall (Xy000:a) (Xz0:a), (((and (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))) (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->(((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy000)
% Found (x100 x5) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x5) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x5) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x5) as proof of ((Xp Xy0) Xy000)
% Found x60:=(x6 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (x6 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)) as proof of ((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (and_rect20 (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (forall (Xy000:a), (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))->((((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))->P)))=> (((((and_rect (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00)))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))) (fun (x6:(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (x7:(((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))=> (x6 x50)))) as proof of (forall (Xx00:a) (Xy000:a), (a->(((and (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))) (((Xr Xx0) Xy00)->((and ((Xp Xy000) Xy0)) ((Xp Xy0) Xy00))))->(((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x50 as proof of ((Xr Xy0) Xy00)
% Found (x100 x50) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x50) as proof of ((Xp Xy0) Xy00)
% Found x6000:=(x600 x50):((Xp Xx0) Xy00)
% Found (x600 x50) as proof of ((Xp Xx0) Xy00)
% Found ((x60 Xx00) x50) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50) as proof of ((Xp Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x100 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x10 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x1 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x50:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x50 as proof of ((Xr Xy01) Xy00)
% Found (x100 x50) as proof of ((Xp Xy01) Xy00)
% Found ((x10 Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found x6000:=(x600 x50):((Xp Xx0) Xy00)
% Found (x600 x50) as proof of ((Xp Xx0) Xy00)
% Found ((x60 Xx00) x50) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50) as proof of ((Xp Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x300 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x50:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x50 as proof of ((Xr Xy01) Xy00)
% Found (x300 x50) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found x700:=(x70 x50):((Xr Xx0) Xz0)
% Found (x70 x50) as proof of ((Xr Xx0) Xz0)
% Found ((x7 Xy00) x50) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))))
% Found x7000:=(x700 x30):((Xp Xx00) Xz0)
% Found (x700 x30) as proof of ((Xp Xx00) Xz0)
% Found ((x70 Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->((Xp Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect2 ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0)))) P) x6) x5)) ((Xp Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))=> (((x7 Xx00) Xy00) x30)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xz0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x310 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x31 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x30:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xy00:a
% Found x30 as proof of ((Xr Xx00) Xy01)
% Found (x310 x30) as proof of ((Xp Xx00) Xy01)
% Found ((x31 Xy01) x30) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x30) as proof of ((Xp Xx00) Xy01)
% Found (((x3 Xx00) Xy01) x30) as proof of ((Xp Xx00) Xy01)
% Found x700:=(x70 x50):((Xr Xx0) Xz0)
% Found (x70 x50) as proof of ((Xr Xx0) Xz0)
% Found ((x7 Xy00) x50) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))))
% Found x6000:=(x600 x50):((Xp Xx0) Xy00)
% Found (x600 x50) as proof of ((Xp Xx0) Xy00)
% Found ((x60 Xx00) x50) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50) as proof of ((Xp Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x300 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x50:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x50 as proof of ((Xr Xy01) Xy00)
% Found (x300 x50) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x50) as proof of ((Xp Xy01) Xy00)
% Found x700:=(x70 x50):((Xr Xx0) Xz0)
% Found (x70 x50) as proof of ((Xr Xx0) Xz0)
% Found ((x7 Xy00) x50) as proof of ((Xr Xx0) Xz0)
% Found (fun (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((Xr Xx0) Xz0)
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx0) Xz0))
% Found (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx0) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found ((and_rect2 ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50))) as proof of ((Xr Xx0) Xz0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of ((Xr Xx0) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))
% Found (fun (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0)))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xy00:a) (x50:((Xr Xx0) Xy00))=> (((fun (P:Type) (x6:((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx0) Xz0)) (fun (x6:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x7:(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> ((x7 Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xr Xx0) Xz0))))))
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x50000:=(x5000 x30):((Xp Xx0) Xz0)
% Found (x5000 x30) as proof of ((Xp Xx0) Xz0)
% Found ((x500 Xy00) x30) as proof of ((Xp Xx0) Xz0)
% Found (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x50 Xy000) x301) x400)) Xy00) x30) as proof of ((Xp Xx0) Xz0)
% Found (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30) as proof of ((Xp Xx0) Xz0)
% Found (fun (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)) as proof of ((Xp Xx0) Xz0)
% Found (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->((Xp Xx0) Xz0))
% Found (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)) as proof of ((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->((Xp Xx0) Xz0)))
% Found (and_rect20 (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found ((and_rect2 ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of ((Xp Xx0) Xz0)
% Found (fun (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))
% Found (fun (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))
% Found (fun (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))
% Found (fun (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))
% Found (fun (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))))
% Found (fun (Xx00:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xy00:a) (x30:((Xr Xx0) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))->((forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx0) Xz0)) (fun (x4:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))) (x5:(forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx0) Xy000))=> (((x5 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy0)))))) (forall (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xy0:a), (((Xr Xx0) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))))
% Found x3:((Xr Xx00) Xy0)
% Instantiate: Xy000:=Xx00:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x30000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x3000 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x300 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x300 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x30:((Xr Xx0) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x30 as proof of ((Xr Xx0) Xy000)
% Found (x30000 x30) as proof of ((Xp Xx0) Xy000)
% Found ((x3000 Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x300 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found (((x300 Xx0) Xy000) x30) as proof of ((Xp Xx0) Xy000)
% Found x60000:=(x6000 x40):((Xp Xx00) Xz0)
% Found (x6000 x40) as proof of ((Xp Xx00) Xz0)
% Found ((x600 Xy00) x40) as proof of ((Xp Xx00) Xz0)
% Found (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> (((x60 Xy000) x401) x400)) Xy00) x40) as proof of ((Xp Xx00) Xz0)
% Found (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40) as proof of ((Xp Xx00) Xz0)
% Found (fun (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))->((Xp Xx00) Xz0))
% Found (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))->((Xp Xx00) Xz0)))
% Found (and_rect20 (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect2 ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))
% Found (fun (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))
% Found (fun (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))
% Found (fun (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))
% Found (fun (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))) P) x5) x4)) ((Xp Xx00) Xz0)) (fun (x5:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0))))) (x6:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))=> (((fun (Xy000:a) (x401:((Xr Xx00) Xy000))=> ((((x6 Xx00) Xy000) x401) x400)) Xy00) x40)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))))))
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x4 as proof of ((Xr Xy000) Xy0)
% Found (x300 x4) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found x40:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x40 as proof of ((Xr Xx00) Xy000)
% Found (x300 x40) as proof of ((Xp Xx00) Xy000)
% Found ((x30 Xy000) x40) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x40) as proof of ((Xp Xx00) Xy000)
% Found (((x3 Xx00) Xy000) x40) as proof of ((Xp Xx00) Xy000)
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x3 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x600:=(x60 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (x60 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found ((x6 Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))->((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))
% Found (and_rect20 (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xy00:a), (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x600:=(x60 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (x60 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found ((x6 Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))->((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))
% Found (and_rect20 (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xy00:a), (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x300 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x300 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x6000:=(x600 x30):((Xp Xx0) Xy00)
% Found (x600 x30) as proof of ((Xp Xx0) Xy00)
% Found ((x60 Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (((Xr Xx00) Xy00)->((Xp Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) P) x6) x5)) ((Xp Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x30)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx0) Xy0))))))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy01)
% Found (x310 x5) as proof of ((Xp Xx0) Xy01)
% Found ((x31 Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found (((x3 Xx0) Xy01) x5) as proof of ((Xp Xx0) Xy01)
% Found x30:((Xr Xx00) Xy00)
% Instantiate: Xy01:=Xx00:a
% Found x30 as proof of ((Xr Xy01) Xy00)
% Found (x310 x30) as proof of ((Xp Xy01) Xy00)
% Found ((x31 Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x30) as proof of ((Xp Xy01) Xy00)
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy000) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xy000) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xy0) Xz0)
% Found (fun (x8:((Xp Xy0) Xz0))=> x8) as proof of ((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x6:((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xz0))=> x6) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x5:((Xp Xx00) Xy00)
% Found (fun (x6:((Xp Xy01) Xy00))=> x5) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy000) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xy000) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x8:((Xp Xy0) Xz0)
% Found (fun (x8:((Xp Xy0) Xz0))=> x8) as proof of ((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x600:=(x60 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (x60 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found ((x6 Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)) as proof of ((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))->((forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))
% Found (and_rect20 (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xy00:a), (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xy0000:a), (((Xr Xx0) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> ((x6 Xy000) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00)))))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy000) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xy000) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xy0) Xz0)
% Found (fun (x8:((Xp Xy0) Xz0))=> x8) as proof of ((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x30:=(x3 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x3 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (x3 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (x5:((Xr Xx00) Xy00))=> (x3 Xx0)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found x30:=(x3 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x3 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (x10 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found ((x1 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x3 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x3 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy000) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xy000) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x8:((Xp Xy0) Xz0)
% Found (fun (x8:((Xp Xy0) Xz0))=> x8) as proof of ((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x6:((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xz0))=> x6) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x5) x4)) ((Xp Xy00) Xz0)) (fun (x5:((Xp Xy00) Xy01)) (x6:((Xp Xy00) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x5:((Xp Xx00) Xy00)
% Found (fun (x6:((Xp Xy01) Xy00))=> x5) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x5) x4)) ((Xp Xx00) Xy00)) (fun (x5:((Xp Xx00) Xy00)) (x6:((Xp Xy01) Xy00))=> x5))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xz0))=> x7) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x6) x5)) ((Xp Xy00) Xz0)) (fun (x6:((Xp Xy00) Xy01)) (x7:((Xp Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x6:((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xy01) Xy00))=> x6) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x6) x5)) ((Xp Xx00) Xy00)) (fun (x6:((Xp Xx00) Xy00)) (x7:((Xp Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x50000:=(x5000 x40):((Xp Xx0) Xy00)
% Found (x5000 x40) as proof of ((Xp Xx0) Xy00)
% Found ((x500 Xx00) x40) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> (((x50 Xx000) x401) x400)) Xx00) x40) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40) as proof of ((Xp Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))->((Xp Xx0) Xy00))
% Found (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))
% Found (fun (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))
% Found (fun (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))
% Found (fun (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))
% Found (fun (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))
% Found (fun (Xy0:a) (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x4:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))) (Xx00:a) (Xy00:a) (x40:((Xr Xx00) Xy00)) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x5:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00))))) P) x5) x4)) ((Xp Xx0) Xy00)) (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000))))) (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))=> (((fun (Xx000:a) (x401:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x5 Xx000) Xy00)) Xx000) x401) x400)) Xx00) x40)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00)))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))))
% Found x40:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x40 as proof of ((Xr Xy000) Xy00)
% Found (x300 x40) as proof of ((Xp Xy000) Xy00)
% Found ((x30 Xy00) x40) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x40) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x40) as proof of ((Xp Xy000) Xy00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x4 as proof of ((Xr Xx0) Xy000)
% Found (x300 x4) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy000) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xy000) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xy0) Xz0)
% Found (fun (x8:((Xp Xy0) Xz0))=> x8) as proof of ((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x3 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x7000:=(x700 x50):((Xr Xx00) Xz0)
% Found (x700 x50) as proof of ((Xr Xx00) Xz0)
% Found ((x70 Xy00) x50) as proof of ((Xr Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x50) as proof of ((Xr Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((Xr Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found ((and_rect2 ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of ((Xr Xx00) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xr Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0))))))
% Found x7000:=(x700 x50):((Xr Xx00) Xz0)
% Found (x700 x50) as proof of ((Xr Xx00) Xz0)
% Found ((x70 Xy00) x50) as proof of ((Xr Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x50) as proof of ((Xr Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((Xr Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found ((and_rect2 ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of ((Xr Xx00) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xr Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0))))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((Xp Xx00) Xy0)
% Found (fun (x8:((Xp Xy000) Xy0))=> x7) as proof of ((Xp Xx00) Xy0)
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xy000) Xy0)->((Xp Xx00) Xy0))
% Found (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7) as proof of (((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->((Xp Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found ((and_rect2 ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy0)->(((Xp Xy000) Xy0)->P)))=> (((((and_rect ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0)) P) x7) x6)) ((Xp Xx00) Xy0)) (fun (x7:((Xp Xx00) Xy0)) (x8:((Xp Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x8:((Xp Xy0) Xz0)
% Found (fun (x8:((Xp Xy0) Xz0))=> x8) as proof of ((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8) as proof of (((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy0) Xy000)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0)) P) x7) x6)) ((Xp Xy0) Xz0)) (fun (x7:((Xp Xy0) Xy000)) (x8:((Xp Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x3 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x7000:=(x700 x50):((Xr Xx00) Xz0)
% Found (x700 x50) as proof of ((Xr Xx00) Xz0)
% Found ((x70 Xy00) x50) as proof of ((Xr Xx00) Xz0)
% Found (((x7 Xx00) Xy00) x50) as proof of ((Xr Xx00) Xz0)
% Found (fun (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((Xr Xx00) Xz0)
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx00) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->((Xr Xx00) Xz0)))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found ((and_rect2 ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50))) as proof of ((Xr Xx00) Xz0)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of ((Xr Xx00) Xz0)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xr Xx00) Xz0))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0)))) P) x6) x5)) ((Xr Xx00) Xz0)) (fun (x6:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xr Xx000) Xy0)))) (x7:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))=> (((x7 Xx00) Xy00) x50)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xx0) Xz0))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx00) Xz0))))))
% Found x500000:=(x50000 x30):((Xp Xx00) Xz0)
% Found (x50000 x30) as proof of ((Xp Xx00) Xz0)
% Found ((x5000 Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> (((x500 Xy000) x301) x400)) Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> (((x50 Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30) as proof of ((Xp Xx00) Xz0)
% Found (fun (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)) as proof of ((Xp Xx00) Xz0)
% Found (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)) as proof of ((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))->((Xp Xx00) Xz0))
% Found (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)) as proof of ((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0)))))->((Xp Xx00) Xz0)))
% Found (and_rect20 (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found ((and_rect2 ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of ((Xp Xx00) Xz0)
% Found (fun (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))
% Found (fun (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))
% Found (fun (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))
% Found (fun (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))))
% Found (fun (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))))
% Found (fun (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))->((forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0)))))) P) x4) x3)) ((Xp Xx00) Xz0)) (fun (x4:(forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((forall (Xx0000:a) (Xy000:a), (((Xr Xx0000) Xy000)->((Xp Xx0000) Xy000)))->((forall (Xx0000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx0000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx0000) Xz00)))->((Xp Xx000) Xy0)))))) (x5:(forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xz0))))))=> (((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((fun (Xy000:a) (x301:((Xr Xx00) Xy000))=> ((((x5 Xx00) Xy000) x301) x300)) Xy000) x301) x400)) Xy00) x30)))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx00) Xy0)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xx0) Xz0))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx00) Xz0))))))))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x30000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x3000 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x300 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x300 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x30:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xy00:a
% Found x30 as proof of ((Xr Xx00) Xy000)
% Found (x30000 x30) as proof of ((Xp Xx00) Xy000)
% Found ((x3000 Xy000) x30) as proof of ((Xp Xx00) Xy000)
% Found (((x300 Xx00) Xy000) x30) as proof of ((Xp Xx00) Xy000)
% Found (((x300 Xx00) Xy000) x30) as proof of ((Xp Xx00) Xy000)
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x300 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x300:=(x30 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x30 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found x300:=(x30 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x30 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (x10 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x1 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x3 Xx0) Xy00))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x300:=(x30 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x30 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found x300:=(x30 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x30 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (x20 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x2 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01))=> ((x3 Xx0) Xy00))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x3 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x7:((Xp Xx00) Xy00)
% Found (fun (x8:((Xp Xy01) Xy00))=> x7) as proof of ((Xp Xx00) Xy00)
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xy01) Xy00)->((Xp Xx00) Xy00))
% Found (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7) as proof of (((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->((Xp Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found ((and_rect2 ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7)) as proof of ((Xp Xx00) Xy00)
% Found (fun (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of ((Xp Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00))->((Xp Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xp Xx00) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xp Xx00) Xy00)->(((Xp Xy01) Xy00)->P)))=> (((((and_rect ((Xp Xx00) Xy00)) ((Xp Xy01) Xy00)) P) x7) x6)) ((Xp Xx00) Xy00)) (fun (x7:((Xp Xx00) Xy00)) (x8:((Xp Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xp Xx0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xx0) Xy00))))
% Found x8:((Xp Xy00) Xz0)
% Found (fun (x8:((Xp Xy00) Xz0))=> x8) as proof of ((Xp Xy00) Xz0)
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xz0)->((Xp Xy00) Xz0))
% Found (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8) as proof of (((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->((Xp Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found ((and_rect2 ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8)) as proof of ((Xp Xy00) Xz0)
% Found (fun (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of ((Xp Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xp Xy00) Xy01)->(((Xp Xy00) Xz0)->P)))=> (((((and_rect ((Xp Xy00) Xy01)) ((Xp Xy00) Xz0)) P) x7) x6)) ((Xp Xy00) Xz0)) (fun (x7:((Xp Xy00) Xy01)) (x8:((Xp Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xp Xy00) Xy0)) ((Xp Xy00) Xz0))->((Xp Xy00) Xz0))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x6000:=(x600 x50):((Xr Xx0) Xy00)
% Found (x600 x50) as proof of ((Xr Xx0) Xy00)
% Found ((x60 Xx00) x50) as proof of ((Xr Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50) as proof of ((Xr Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((Xr Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found ((and_rect2 ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of ((Xr Xx0) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xr Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x6000:=(x600 x50):((Xr Xx0) Xy00)
% Found (x600 x50) as proof of ((Xr Xx0) Xy00)
% Found ((x60 Xx00) x50) as proof of ((Xr Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50) as proof of ((Xr Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((Xr Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found ((and_rect2 ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of ((Xr Xx0) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xr Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x300 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x300 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x100:=(x10 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x300:=(x30 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x700:=(x70 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (x70 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((x7 Xy000) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x700:=(x70 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (x70 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((x7 Xy000) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x3 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x6000:=(x600 x50):((Xr Xx0) Xy00)
% Found (x600 x50) as proof of ((Xr Xx0) Xy00)
% Found ((x60 Xx00) x50) as proof of ((Xr Xx0) Xy00)
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50) as proof of ((Xr Xx0) Xy00)
% Found (fun (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((Xr Xx0) Xy00)
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx0) Xy00))
% Found (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))->((Xr Xx0) Xy00)))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found ((and_rect2 ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50))) as proof of ((Xr Xx0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of ((Xr Xx0) Xy00)
% Found (fun (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((Xr Xx00) Xy00)->((Xr Xx0) Xy00))
% Found (fun (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))
% Found (fun (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0)))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (Xx00:a) (Xy00:a) (x50:((Xr Xx00) Xy00))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) P) x6) x5)) ((Xr Xx0) Xy00)) (fun (x6:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy000)))) (x7:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy00)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx0) Xy00)))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((Xr Xx0) Xy0))))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x401000:=(x40100 x30):((Xp Xx0) Xy00)
% Found (x40100 x30) as proof of ((Xp Xx0) Xy00)
% Found ((x4010 Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> (((x401 Xx000) x301) x400)) Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> (((x40 Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30) as proof of ((Xp Xx0) Xy00)
% Found (fun (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)) as proof of ((Xp Xx0) Xy00)
% Found (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))->((Xp Xx0) Xy00))
% Found (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)) as proof of ((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000)))))->((Xp Xx0) Xy00)))
% Found (and_rect20 (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found ((and_rect2 ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of ((Xp Xx0) Xy00)
% Found (fun (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of ((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))
% Found (fun (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00)))
% Found (fun (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy00))))
% Found (fun (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (forall (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))
% Found (fun (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))
% Found (fun (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))))
% Found (fun (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0)))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (forall (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))))))
% Found (fun (Xx0:a) (Xy0:a) (Xz0:a) (x3:((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))) (Xx00:a) (Xy00:a) (x30:((Xr Xx00) Xy00)) (x300:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))) (x400:(forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00))))=> (((fun (P:Type) (x4:((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))->((forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy00)))))) P) x4) x3)) ((Xp Xx0) Xy00)) (fun (x4:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz0:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy000)))))) (x5:(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((forall (Xx000:a) (Xy0000:a), (((Xr Xx000) Xy0000)->((Xp Xx000) Xy0000)))->((forall (Xx000:a) (Xy0000:a) (Xz00:a), (((and ((Xp Xx000) Xy0000)) ((Xp Xy0000) Xz00))->((Xp Xx000) Xz00)))->((Xp Xy0) Xy000))))))=> (((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a) (x301:((Xr Xx000) Xy00))=> ((((fun (Xx000:a)=> ((x4 Xx000) Xy00)) Xx000) x301) x300)) Xx000) x301) x400)) Xx00) x30)))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((Xp Xx000) Xy000)))->((forall (Xx000:a) (Xy000:a) (Xz0:a), (((and ((Xp Xx000) Xy000)) ((Xp Xy000) Xz0))->((Xp Xx000) Xz0)))->((Xp Xx0) Xy00)))))) (forall (Xx0:a) (Xy00:a), (((Xr Xx0) Xy00)->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy000)))->((forall (Xx00:a) (Xy000:a) (Xz00:a), (((and ((Xp Xx00) Xy000)) ((Xp Xy000) Xz00))->((Xp Xx00) Xz00)))->((Xp Xy0) Xy00))))))->(forall (Xx00:a) (Xy0:a), (((Xr Xx00) Xy0)->((forall (Xx000:a) (Xy00:a), (((Xr Xx000) Xy00)->((Xp Xx000) Xy00)))->((forall (Xx000:a) (Xy00:a) (Xz00:a), (((and ((Xp Xx000) Xy00)) ((Xp Xy00) Xz00))->((Xp Xx000) Xz00)))->((Xp Xx0) Xy0))))))))
% Found x30:((Xr Xx00) Xy00)
% Instantiate: Xy000:=Xx00:a
% Found x30 as proof of ((Xr Xy000) Xy00)
% Found (x30000 x30) as proof of ((Xp Xy000) Xy00)
% Found ((x3000 Xy00) x30) as proof of ((Xp Xy000) Xy00)
% Found (((x300 Xy000) Xy00) x30) as proof of ((Xp Xy000) Xy00)
% Found (((x300 Xy000) Xy00) x30) as proof of ((Xp Xy000) Xy00)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x30000 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x3000 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x300 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x300 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x3 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found x100:=(x10 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x700:=(x70 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (x70 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((x7 Xy000) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)) as proof of ((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((fun (P:Type) (x6:((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> ((x7 Xy000) x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))))
% Found x30:=(x3 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x3 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x3 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x3 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x300 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x300 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x7:((Xp Xy0) Xz)
% Found (fun (x7:((Xp Xy0) Xz))=> x7) as proof of ((Xp Xy0) Xz)
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->((Xp Xy0) Xz))
% Found (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7) as proof of (((Xp Xy0) Xz)->(((Xp Xy0) Xz)->((Xp Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found ((and_rect2 ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7)) as proof of ((Xp Xy0) Xz)
% Found (fun (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of ((Xp Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xz)->(((Xp Xy0) Xz)->P)))=> (((((and_rect ((Xp Xy0) Xz)) ((Xp Xy0) Xz)) P) x6) x5)) ((Xp Xy0) Xz)) (fun (x6:((Xp Xy0) Xz)) (x7:((Xp Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xp Xy0) Xz)) ((Xp Xy0) Xz))->((Xp Xy0) Xz)))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x7:((Xp Xy0) Xz0)
% Found (fun (x7:((Xp Xy0) Xz0))=> x7) as proof of ((Xp Xy0) Xz0)
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xz0)->((Xp Xy0) Xz0))
% Found (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7) as proof of (((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->((Xp Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found ((and_rect2 ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7)) as proof of ((Xp Xy0) Xz0)
% Found (fun (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of ((Xp Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xp Xy0) Xy00)->(((Xp Xy0) Xz0)->P)))=> (((((and_rect ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0)) P) x6) x5)) ((Xp Xy0) Xz0)) (fun (x6:((Xp Xy0) Xy00)) (x7:((Xp Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0))))
% Found x6:((Xp Xx0) Xy0)
% Found (fun (x7:((Xp Xy00) Xy0))=> x6) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xy00) Xy0)->((Xp Xx0) Xy0))
% Found (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6) as proof of (((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->((Xp Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found ((and_rect2 ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6)) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xp Xx0) Xy0)->(((Xp Xy00) Xy0)->P)))=> (((((and_rect ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0)) P) x6) x5)) ((Xp Xx0) Xy0)) (fun (x6:((Xp Xx0) Xy0)) (x7:((Xp Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx0) Xy0))))
% Found x100:=(x10 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x300:=(x30 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x3 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy000) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xy000) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xy0) Xz0)
% Found (fun (x8:((Xr Xy0) Xz0))=> x8) as proof of ((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy000) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xy000) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xy0) Xz0)
% Found (fun (x8:((Xr Xy0) Xz0))=> x8) as proof of ((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x6:((Xr Xy00) Xz0)
% Found (fun (x6:((Xr Xy00) Xz0))=> x6) as proof of ((Xr Xy00) Xz0)
% Found (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x7:((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xz0))=> x7) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x5:((Xr Xx00) Xy00)
% Found (fun (x6:((Xr Xy01) Xy00))=> x5) as proof of ((Xr Xx00) Xy00)
% Found (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found x6:((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xy01) Xy00))=> x6) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy000) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xy000) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xy0) Xz0)
% Found (fun (x8:((Xr Xy0) Xz0))=> x8) as proof of ((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy000) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xy000) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x8:((Xr Xy0) Xz0)
% Found (fun (x8:((Xr Xy0) Xz0))=> x8) as proof of ((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x6:((Xr Xy00) Xz0)
% Found (fun (x6:((Xr Xy00) Xz0))=> x6) as proof of ((Xr Xy00) Xz0)
% Found (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x5:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x5) x4)) ((Xr Xy00) Xz0)) (fun (x5:((Xr Xy00) Xy01)) (x6:((Xr Xy00) Xz0))=> x6))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x5:((Xr Xx00) Xy00)
% Found (fun (x6:((Xr Xy01) Xy00))=> x5) as proof of ((Xr Xx00) Xy00)
% Found (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x4:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x5:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x5) x4)) ((Xr Xx00) Xy00)) (fun (x5:((Xr Xx00) Xy00)) (x6:((Xr Xy01) Xy00))=> x5))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x7:((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xz0))=> x7) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x6) x5)) ((Xr Xy00) Xz0)) (fun (x6:((Xr Xy00) Xy01)) (x7:((Xr Xy00) Xz0))=> x7))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x6:((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xy01) Xy00))=> x6) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x6:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x6) x5)) ((Xr Xx00) Xy00)) (fun (x6:((Xr Xx00) Xy00)) (x7:((Xr Xy01) Xy00))=> x6))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx0) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))
% Found x10:=(x1 Xx0):(forall (Xy0:a), (((Xr Xx0) Xy0)->((Xp Xx0) Xy0)))
% Found (x1 Xx0) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00))=> (x1 Xx0))) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))))=> (x1 Xx0)))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x3 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x300:=(x30 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x30 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x3 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x7000:=(x700 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (x700 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found ((x70 Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (((x7 Xx00) Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x7:((Xr Xy0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x7) as proof of ((Xr Xy0) Xz)
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->((Xr Xy0) Xz))
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->(((Xr Xy0) Xz)->((Xr Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found ((and_rect2 ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (fun (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of ((Xr Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))))
% Found x7:((Xr Xx) Xy0)
% Found (fun (x7:((Xr Xx) Xy0))=> x7) as proof of ((Xr Xx) Xy0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->((Xr Xx) Xy0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xy0)->((Xr Xx) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found ((and_rect2 ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of ((Xr Xx) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))))
% Found x7000:=(x700 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (x700 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found ((x70 Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (((x7 Xx00) Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x7:((Xr Xy0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x7) as proof of ((Xr Xy0) Xz)
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->((Xr Xy0) Xz))
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->(((Xr Xy0) Xz)->((Xr Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found ((and_rect2 ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (fun (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of ((Xr Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))))
% Found x100:=(x10 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x7:((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xz0))=> x7) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x7:((Xr Xx) Xy0)
% Found (fun (x7:((Xr Xx) Xy0))=> x7) as proof of ((Xr Xx) Xy0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->((Xr Xx) Xy0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xy0)->((Xr Xx) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found ((and_rect2 ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of ((Xr Xx) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))))
% Found x6:((Xr Xx0) Xy0)
% Found (fun (x7:((Xr Xy00) Xy0))=> x6) as proof of ((Xr Xx0) Xy0)
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xy00) Xy0)->((Xr Xx0) Xy0))
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found ((and_rect2 ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x7:((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xz0))=> x7) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x8:((Xr Xy0) Xz0)
% Found (fun (x8:((Xr Xy0) Xz0))=> x8) as proof of ((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x6:((Xr Xx0) Xy0)
% Found (fun (x7:((Xr Xy00) Xy0))=> x6) as proof of ((Xr Xx0) Xy0)
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xy00) Xy0)->((Xr Xx0) Xy0))
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found ((and_rect2 ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy000) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xy000) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x8:((Xr Xy0) Xz0)
% Found (fun (x8:((Xr Xy0) Xz0))=> x8) as proof of ((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8) as proof of (((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy0) Xy000)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0)) P) x7) x6)) ((Xr Xy0) Xz0)) (fun (x7:((Xr Xy0) Xy000)) (x8:((Xr Xy0) Xz0))=> x8))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x7:((Xr Xx00) Xy0)
% Found (fun (x8:((Xr Xy000) Xy0))=> x7) as proof of ((Xr Xx00) Xy0)
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xy000) Xy0)->((Xr Xx00) Xy0))
% Found (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7) as proof of (((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->((Xr Xx00) Xy0)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found ((and_rect2 ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7)) as proof of ((Xr Xx00) Xy0)
% Found (fun (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy0)->(((Xr Xy000) Xy0)->P)))=> (((((and_rect ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0)) P) x7) x6)) ((Xr Xx00) Xy0)) (fun (x7:((Xr Xx00) Xy0)) (x8:((Xr Xy000) Xy0))=> x7))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x7000:=(x700 x50):((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (x700 x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found ((x70 Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (((x7 Xx00) Xy000) x50) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)) as proof of ((forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (and_rect20 (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found ((and_rect2 ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (forall (Xy00:a) (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))->((forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0))))) P) x6) x5)) ((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0))) (fun (x6:(forall (Xx000:a) (Xy000:a), (((Xr Xx000) Xy000)->((and ((Xp Xx000) Xy0)) ((Xp Xy0) Xy00))))) (x7:(forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))=> (((x7 Xx00) Xy000) x50)))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xy00))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xz0)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx00) Xy0)) ((Xp Xy0) Xz0)))))))
% Found x7:((Xr Xy0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x7) as proof of ((Xr Xy0) Xz)
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->((Xr Xy0) Xz))
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->(((Xr Xy0) Xz)->((Xr Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found ((and_rect2 ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (fun (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of ((Xr Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))))
% Found x7:((Xr Xx) Xy0)
% Found (fun (x7:((Xr Xx) Xy0))=> x7) as proof of ((Xr Xx) Xy0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->((Xr Xx) Xy0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xy0)->((Xr Xx) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found ((and_rect2 ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of ((Xr Xx) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x7:((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xz0))=> x7) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x6:((Xr Xx0) Xy0)
% Found (fun (x7:((Xr Xy00) Xy0))=> x6) as proof of ((Xr Xx0) Xy0)
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xy00) Xy0)->((Xr Xx0) Xy0))
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found ((and_rect2 ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x6000:=(x600 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (x600 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found ((x60 Xx00) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))->((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xy00:a), (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))))
% Found x6000:=(x600 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (x600 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found ((x60 Xx00) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))->((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xy00:a), (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))))
% Found x7:((Xr Xx00) Xy00)
% Found (fun (x8:((Xr Xy01) Xy00))=> x7) as proof of ((Xr Xx00) Xy00)
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xy01) Xy00)->((Xr Xx00) Xy00))
% Found (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7) as proof of (((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->((Xr Xx00) Xy00)))
% Found (and_rect20 (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found ((and_rect2 ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7)) as proof of ((Xr Xx00) Xy00)
% Found (fun (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of ((Xr Xx00) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00))->((Xr Xx00) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xy0:a), (a->(((and ((Xr Xx00) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx00) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)))=> (((fun (P:Type) (x7:(((Xr Xx00) Xy00)->(((Xr Xy01) Xy00)->P)))=> (((((and_rect ((Xr Xx00) Xy00)) ((Xr Xy01) Xy00)) P) x7) x6)) ((Xr Xx00) Xy00)) (fun (x7:((Xr Xx00) Xy00)) (x8:((Xr Xy01) Xy00))=> x7))) as proof of (forall (Xx0:a) (Xy0:a), (a->(((and ((Xr Xx0) Xy00)) ((Xr Xy0) Xy00))->((Xr Xx0) Xy00))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))))=> ((x1 Xx0) Xy00))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x8:((Xr Xy00) Xz0)
% Found (fun (x8:((Xr Xy00) Xz0))=> x8) as proof of ((Xr Xy00) Xz0)
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xz0)->((Xr Xy00) Xz0))
% Found (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8) as proof of (((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->((Xr Xy00) Xz0)))
% Found (and_rect20 (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found ((and_rect2 ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8)) as proof of ((Xr Xy00) Xz0)
% Found (fun (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of ((Xr Xy00) Xz0)
% Found (fun (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xz0:a), (((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)))=> (((fun (P:Type) (x7:(((Xr Xy00) Xy01)->(((Xr Xy00) Xz0)->P)))=> (((((and_rect ((Xr Xy00) Xy01)) ((Xr Xy00) Xz0)) P) x7) x6)) ((Xr Xy00) Xz0)) (fun (x7:((Xr Xy00) Xy01)) (x8:((Xr Xy00) Xz0))=> x8))) as proof of (a->(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy00) Xy0)) ((Xr Xy00) Xz0))->((Xr Xy00) Xz0))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found x100:=(x10 Xy00):(((Xr Xx0) Xy00)->((Xp Xx0) Xy00))
% Found (x10 Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy00) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00))) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000))=> ((x1 Xx0) Xy00))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))))=> ((x1 Xx0) Xy00)))) as proof of (((Xr Xx0) Xy00)->((Xp Xx0) Xy0))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x100:=(x10 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x6000:=(x600 x50):((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (x600 x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found ((x60 Xx00) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)) as proof of ((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))->((forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000))))->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))
% Found (and_rect20 (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found ((and_rect2 ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000)))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))
% Found (fun (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xy00:a), (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((fun (P:Type) (x6:((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))->((forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))->P)))=> (((((and_rect (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000))))) P) x6) x5)) ((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))) (fun (x6:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy0000))))) (x7:(forall (Xx00:a) (Xy0000:a), (((Xr Xx00) Xy0000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy0000)))))=> (((fun (Xx000:a)=> ((x6 Xx000) Xy000)) Xx00) x50)))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy000))))) (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((and ((Xp Xy00) Xy0)) ((Xp Xy0) Xy000)))))->(forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((and ((Xp Xx0) Xy0)) ((Xp Xy0) Xy00)))))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found (x1 Xx00) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy01)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy01))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy01)))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy0))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy01)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy01))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy01)))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (x10 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found ((x1 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x1 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy0))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (x20 ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found ((x2 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy01:a), (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz0))->((Xp Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xp Xy0) Xy000)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xz00))->((Xp Xy0) Xz00)))))))))
% Found x10:=(x1 Xx00):(forall (Xy0:a), (((Xr Xx00) Xy0)->((Xp Xx00) Xy0)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found (x1 Xx00) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy000)))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy0)))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xp Xx0) Xy0)) ((Xp Xy000) Xy0))->((Xp Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xp Xx00) Xy0)) ((Xp Xy00) Xy0))->((Xp Xx00) Xy0)))))))))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (x10 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found ((x1 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy000)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy000))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy000)))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy0))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x100:=(x10 Xy000):(((Xr Xx0) Xy000)->((Xp Xx0) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found ((x1 Xx0) Xy000) as proof of (((Xr Xx0) Xy000)->((Xp Xx0) Xy0))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x70 as proof of ((Xr Xx00) Xy0)
% Found (x100 x70) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x70) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x70) as proof of ((Xp Xx00) Xy0)
% Found (fun (x70:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x70)) as proof of ((Xp Xx00) Xy0)
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x70 as proof of ((Xr Xy0) Xy000)
% Found (x100 x70) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x70) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x70) as proof of ((Xp Xy0) Xy000)
% Found (fun (x70:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x70)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x70:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x70)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))
% Found x1000:=(x100 x5):((Xp Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found (((conj2 (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)))) as proof of ((Xp Xx0) Xy0)
% Found ((x4 (fun (x8:a) (x70:a)=> ((Xp Xx0) Xy0))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> ((x4 (fun (x8:a) (x70:a)=> ((Xp Xx0) Xy0))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))))) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy01)->((Xp Xy0) Xy00))
% Found (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))
% Found x1000:=(x100 x5):((Xp Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found (((conj2 (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found (x30 ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)))) as proof of ((Xp Xy0) Xy00)
% Found ((x3 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)))) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> ((x3 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))))) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> ((x3 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a;Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xy01) Xy00)
% Found (x100 x5) as proof of ((Xp Xy01) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x1 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x100 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x70 as proof of ((Xr Xx00) Xy0)
% Found (x300 x70) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x70) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x70) as proof of ((Xp Xx00) Xy0)
% Found (fun (x70:((Xr Xx00) Xy000))=> (((x3 Xx00) Xy0) x70)) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a;Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x100 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x100 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x6)) as proof of ((Xp Xx00) Xy0)
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x70 as proof of ((Xr Xy0) Xy000)
% Found (x300 x70) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x70) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x70) as proof of ((Xp Xy0) Xy000)
% Found (fun (x70:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x70)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x70:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x70)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))
% Found x3000:=(x300 x5):((Xp Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)) as proof of (a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)) as proof of (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found (((conj2 (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found (x20 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)))) as proof of ((Xp Xx0) Xy0)
% Found ((x2 (fun (x8:a) (x70:a)=> ((Xp Xx0) Xy0))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> ((x2 (fun (x8:a) (x70:a)=> ((Xp Xx0) Xy0))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x3 Xx0) Xy0) x5))))) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy01)->((Xp Xy0) Xy00))
% Found (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5)) as proof of (forall (Xy01:a), (((Xr Xx00) Xy01)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5)) as proof of (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))
% Found x3000:=(x300 x5):((Xp Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))
% Found (fun (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)) as proof of (a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)) as proof of (a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)) as proof of (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))
% Found ((conj20 (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found (((conj2 (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found (x10 ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)))) as proof of ((Xp Xy0) Xy00)
% Found ((x1 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5)))) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> ((x1 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5))))) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> ((x1 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy01:a), (((Xr Xx0) Xy01)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy01:a) (x6:((Xr Xx00) Xy01))=> (((x3 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy01:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x3 Xy0) Xy00) x5))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a;Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xy01) Xy00)
% Found (x300 x5) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a;Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x300 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x3 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x300 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x6)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x6)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x300 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x3 Xx00) Xy0) x6)) as proof of ((Xp Xx00) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a;Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy00)
% Found (x3000 x3) as proof of ((Xp Xy000) Xy00)
% Found ((x300 Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found (((x30 Xy000) Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a;Xy000:=Xx0:a
% Found x4 as proof of ((Xr Xy000) Xy00)
% Found (x300 x4) as proof of ((Xp Xy000) Xy00)
% Found ((x30 Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found (((x3 Xy000) Xy00) x4) as proof of ((Xp Xy000) Xy00)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a)=> ((x1 Xx00) Xy000)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x100:=(x10 Xy000):(((Xr Xx00) Xy000)->((Xp Xx00) Xy000))
% Found (x10 Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found ((x1 Xx00) Xy000) as proof of (((Xr Xx00) Xy000)->((Xp Xx00) Xy0))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x70:((Xr Xx00) Xy000))=> x70) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x70:((Xr Xx00) Xy000))=> x70) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x70:((Xr Xx00) Xy000))=> x70) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy01)
% Found (x100 x5) as proof of ((Xp Xy0) Xy01)
% Found ((x10 Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (((x1 Xy0) Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy01) x5)) as proof of ((Xp Xy0) Xy01)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy01) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy01))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy01) x5)) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy01)))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((x1 Xx00) Xy0) x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> (((x1 Xx00) Xy0) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy0))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x70:((Xr Xx00) Xy000))=> x70) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x70:((Xr Xx00) Xy000))=> x70) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x70:((Xr Xx00) Xy000))=> x70) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy01:=Xx0:a;Xy00:=Xy0:a
% Found x5 as proof of ((Xr Xy01) Xy00)
% Found (x300 x5) as proof of ((Xp Xy01) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found (((x3 Xy01) Xy00) x5) as proof of ((Xp Xy01) Xy00)
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy01)
% Found (x300 x5) as proof of ((Xp Xy0) Xy01)
% Found ((x30 Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (((x3 Xy0) Xy01) x5) as proof of ((Xp Xy0) Xy01)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((x3 Xy0) Xy01) x5)) as proof of ((Xp Xy0) Xy01)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> (((x3 Xy0) Xy01) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy01))
% Found (fun (Xy01:a) (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> (((x3 Xy0) Xy01) x5)) as proof of (((Xr Xx00) Xy01)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy01)))
% Found x7:((Xr Xy0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x7) as proof of ((Xr Xy0) Xz)
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->((Xr Xy0) Xz))
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->(((Xr Xy0) Xz)->((Xr Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found ((and_rect2 ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (fun (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of ((Xr Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))))
% Found x5:((Xr Xx00) Xy01)
% Instantiate: Xy0:=Xy01:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x300 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((x3 Xx00) Xy0) x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy01)) (x50:((Xr Xx0) Xy00))=> (((x3 Xx00) Xy0) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy0))
% Found x7:((Xr Xx) Xy0)
% Found (fun (x7:((Xr Xx) Xy0))=> x7) as proof of ((Xr Xx) Xy0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->((Xr Xx) Xy0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xy0)->((Xr Xx) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found ((and_rect2 ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of ((Xr Xx) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))))
% Found x7:((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xz0))=> x7) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x6:((Xr Xx0) Xy0)
% Found (fun (x7:((Xr Xy00) Xy0))=> x6) as proof of ((Xr Xx0) Xy0)
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xy00) Xy0)->((Xr Xx0) Xy0))
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found ((and_rect2 ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x70 as proof of ((Xr Xx00) Xy0)
% Found (x100 x70) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x70) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x70) as proof of ((Xp Xx00) Xy0)
% Found (fun (x70:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x70)) as proof of ((Xp Xx00) Xy0)
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x70 as proof of ((Xr Xy0) Xy000)
% Found (x100 x70) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x70) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x70) as proof of ((Xp Xy0) Xy000)
% Found (fun (x70:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x70)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x70:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x70)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))
% Found x1000:=(x100 x5):((Xp Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)) as proof of (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found (((conj2 (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)))) as proof of ((Xp Xx0) Xy0)
% Found ((x4 (fun (x8:a) (x70:a)=> ((Xp Xx0) Xy0))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5)))) as proof of ((Xp Xx0) Xy0)
% Found (fun (x5:((Xr Xx0) Xy00))=> ((x4 (fun (x8:a) (x70:a)=> ((Xp Xx0) Xy0))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xp Xx0) Xy0)))) (a->(a->(a->(((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0))->((Xp Xx0) Xy0)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xx0) Xy0)) ((Xp Xx0) Xy0)))=> (((x1 Xx0) Xy0) x5))))) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))
% Found x1000:=(x100 x5):((Xp Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))
% Found (fun (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)) as proof of (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found (((conj2 (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found ((((conj (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found ((((conj (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))) as proof of ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00))))))
% Found (x30 ((((conj (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)))) as proof of ((Xp Xy0) Xy00)
% Found ((x3 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5)))) as proof of ((Xp Xy0) Xy00)
% Found (fun (x5:((Xr Xx0) Xy00))=> ((x3 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))))) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00))=> ((x3 (fun (x8:a) (x70:a)=> ((Xp Xy0) Xy00))) ((((conj (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))) (a->(a->(a->(((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00))->((Xp Xy0) Xy00)))))) (fun (Xx00:a) (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5))) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x6:((and ((Xp Xy0) Xy00)) ((Xp Xy0) Xy00)))=> (((x1 Xy0) Xy00) x5))))) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy00))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x6 as proof of ((Xr Xy0) Xy000)
% Found (x100 x6) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x6) as proof of ((Xp Xy0) Xy000)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x6)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a;Xy01:=Xx0:a
% Found x5 as proof of ((Xr Xy01) Xy0)
% Found (x100 x5) as proof of ((Xp Xy01) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found (((x1 Xy01) Xy0) x5) as proof of ((Xp Xy01) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x6 as proof of ((Xr Xx00) Xy0)
% Found (x100 x6) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x6) as proof of ((Xp Xx00) Xy0)
% Found (fun (x6:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x6)) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy000)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xx00) Xy0) x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xx00) Xy0) x5)) as proof of (((Xr Xx0) Xy000)->((Xp Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xx00) Xy0) x5)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xx0) Xy0) x50)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy000)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x300 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x3 Xx00) Xy0) x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x3 Xx00) Xy0) x5)) as proof of (((Xr Xx0) Xy000)->((Xp Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x3 Xx00) Xy0) x5)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x300 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x3 Xx0) Xy0) x50)) as proof of ((Xp Xx0) Xy0)
% Found x7:((Xr Xy0) Xz)
% Found (fun (x7:((Xr Xy0) Xz))=> x7) as proof of ((Xr Xy0) Xz)
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->((Xr Xy0) Xz))
% Found (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7) as proof of (((Xr Xy0) Xz)->(((Xr Xy0) Xz)->((Xr Xy0) Xz)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found ((and_rect2 ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7)) as proof of ((Xr Xy0) Xz)
% Found (fun (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of ((Xr Xy0) Xz)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xz)->(((Xr Xy0) Xz)->P)))=> (((((and_rect ((Xr Xy0) Xz)) ((Xr Xy0) Xz)) P) x6) x5)) ((Xr Xy0) Xz)) (fun (x6:((Xr Xy0) Xz)) (x7:((Xr Xy0) Xz))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xy0) Xz)) ((Xr Xy0) Xz))->((Xr Xy0) Xz)))))
% Found x7:((Xr Xx) Xy0)
% Found (fun (x7:((Xr Xx) Xy0))=> x7) as proof of ((Xr Xx) Xy0)
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->((Xr Xx) Xy0))
% Found (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7) as proof of (((Xr Xx) Xy0)->(((Xr Xx) Xy0)->((Xr Xx) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found ((and_rect2 ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7)) as proof of ((Xr Xx) Xy0)
% Found (fun (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of ((Xr Xx) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx) Xy0)->(((Xr Xx) Xy0)->P)))=> (((((and_rect ((Xr Xx) Xy0)) ((Xr Xx) Xy0)) P) x6) x5)) ((Xr Xx) Xy0)) (fun (x6:((Xr Xx) Xy0)) (x7:((Xr Xx) Xy0))=> x7))) as proof of (a->(a->(a->(((and ((Xr Xx) Xy0)) ((Xr Xx) Xy0))->((Xr Xx) Xy0)))))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz0:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (a->(forall (Xy000:a) (Xz00:a), (((and ((Xr Xy0) Xy000)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xy0) Xy00)))) (a->(forall (Xy00:a) (Xz00:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz00))->((Xr Xy0) Xz00)))))))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x70:((Xr Xx00) Xy000))=> x70) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x70:((Xr Xx00) Xy000))=> x70) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))
% Found (fun (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))
% Found (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7) as proof of (((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))
% Found (and_rect20 (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found ((and_rect2 ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))
% Found (fun (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0))))))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))))=> (((fun (P:Type) (x6:(((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))->(((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))->P)))=> (((((and_rect ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0)))))) P) x6) x5)) ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))) (fun (x6:((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) (x7:((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))=> x7))) as proof of (a->(a->(a->(((and ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy000:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx00) Xy0)))))) ((and (forall (Xx0:a) (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx0) Xy0)))) (forall (Xx0:a) (Xy000:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy000) Xy0))->((Xr Xx0) Xy0))))))->((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->((Xr Xx00) Xy0)))) (forall (Xx00:a) (Xy00:a), (a->(((and ((Xr Xx00) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx00) Xy0)))))))))
% Found x70:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x70:((Xr Xx00) Xy000))=> x70) as proof of ((Xr Xx00) Xy0)
% Found x7:((Xr Xy0) Xz0)
% Found (fun (x7:((Xr Xy0) Xz0))=> x7) as proof of ((Xr Xy0) Xz0)
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xz0)->((Xr Xy0) Xz0))
% Found (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7) as proof of (((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->((Xr Xy0) Xz0)))
% Found (and_rect20 (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found ((and_rect2 ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7)) as proof of ((Xr Xy0) Xz0)
% Found (fun (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of ((Xr Xy0) Xz0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)))=> (((fun (P:Type) (x6:(((Xr Xy0) Xy00)->(((Xr Xy0) Xz0)->P)))=> (((((and_rect ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0)) P) x6) x5)) ((Xr Xy0) Xz0)) (fun (x6:((Xr Xy0) Xy00)) (x7:((Xr Xy0) Xz0))=> x7))) as proof of (a->(forall (Xy00:a) (Xz0:a), (((and ((Xr Xy0) Xy00)) ((Xr Xy0) Xz0))->((Xr Xy0) Xz0))))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy000)
% Found (x100 x5) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x5) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x5) as proof of ((Xp Xy0) Xy000)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy000) x5)) as proof of ((Xp Xy0) Xy000)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy000) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xy0) Xy000))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> (((x1 Xy0) Xy000) x5)) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xp Xy0) Xy000)))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy00))=> (((x1 Xx00) Xy0) x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> (((x1 Xx00) Xy0) x5)) as proof of (((Xr Xx0) Xy00)->((Xp Xx00) Xy0))
% Found x6:((Xr Xx0) Xy0)
% Found (fun (x7:((Xr Xy00) Xy0))=> x6) as proof of ((Xr Xx0) Xy0)
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xy00) Xy0)->((Xr Xx0) Xy0))
% Found (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6) as proof of (((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->((Xr Xx0) Xy0)))
% Found (and_rect20 (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found ((and_rect2 ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6)) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0)))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found (fun (Xx0:a) (Xy00:a) (Xz0:a) (x5:((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)))=> (((fun (P:Type) (x6:(((Xr Xx0) Xy0)->(((Xr Xy00) Xy0)->P)))=> (((((and_rect ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0)) P) x6) x5)) ((Xr Xx0) Xy0)) (fun (x6:((Xr Xx0) Xy0)) (x7:((Xr Xy00) Xy0))=> x6))) as proof of (forall (Xx0:a) (Xy00:a), (a->(((and ((Xr Xx0) Xy0)) ((Xr Xy00) Xy0))->((Xr Xx0) Xy0))))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy0)))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x5 as proof of ((Xr Xy000) Xy0)
% Found (x100 x5) as proof of ((Xp Xy000) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found (((x1 Xy000) Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found (((x1 Xy000) Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x50)) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x50)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x50)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x300 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x30 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x3 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x300 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xx0) Xy0) x5)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy0)))
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy000)
% Found (x100 x5) as proof of ((Xp Xx0) Xy000)
% Found ((x10 Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found (((x1 Xx0) Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found (((x1 Xx0) Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x5 as proof of ((Xr Xy000) Xy0)
% Found (x300 x5) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x300 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x3 Xx00) Xy0) x50)) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x300 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x50)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x50)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x3000 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x300 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x30 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x3000 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x300 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x30 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy000)
% Found (x300 x5) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x4 as proof of ((Xr Xy000) Xy0)
% Found (x300 x4) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x4) as proof of ((Xp Xy000) Xy0)
% Found x4:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x4 as proof of ((Xr Xx0) Xy000)
% Found (x300 x4) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x4) as proof of ((Xp Xx0) Xy000)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy00:=Xy0:a;Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy00)
% Found (x400 x3) as proof of ((Xp Xy000) Xy00)
% Found ((x40 Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found (((x4 Xy000) Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found (((x4 Xy000) Xy00) x3) as proof of ((Xp Xy000) Xy00)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy000)->((Xp Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xy0) Xy00))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx00) Xy0)
% Found (x100 x5) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x5) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xx00) Xy0) x5)) as proof of ((Xp Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xx00) Xy0) x5)) as proof of (((Xr Xx0) Xy000)->((Xp Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> (((x1 Xx00) Xy0) x5)) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xp Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xx0) Xy0) x50)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x5 as proof of ((Xr Xy000) Xy0)
% Found (x300 x5) as proof of ((Xp Xy000) Xy0)
% Found ((x30 Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found (((x3 Xy000) Xy0) x5) as proof of ((Xp Xy000) Xy0)
% Found x5:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x5 as proof of ((Xr Xx0) Xy000)
% Found (x300 x5) as proof of ((Xp Xx0) Xy000)
% Found ((x30 Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found (((x3 Xx0) Xy000) x5) as proof of ((Xp Xx0) Xy000)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found x5 as proof of ((Xr Xy0) Xy00)
% Found (x100 x5) as proof of ((Xp Xy0) Xy00)
% Found ((x10 Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (((x1 Xy0) Xy00) x5) as proof of ((Xp Xy0) Xy00)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of ((Xp Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy00) x5)) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found x5 as proof of ((Xr Xx0) Xy0)
% Found (x100 x5) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x5) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of ((Xp Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (((Xr Xx00) Xy000)->((Xp Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xx0) Xy0) x5)) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xp Xx0) Xy0)))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x50)) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x50)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x50)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xx0) Xy0) x50)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy000)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy000))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy000)))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy0))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x300 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x3 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x3 Xx0) Xy0) x50)) as proof of ((Xp Xx0) Xy0)
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x6:((Xr Xx00) Xy000))=> x6) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x6:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x6:((Xr Xx00) Xy000))=> x6) as proof of ((Xr Xx00) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xx0:a
% Found x3 as proof of ((Xr Xy000) Xy0)
% Found (x400 x3) as proof of ((Xp Xy000) Xy0)
% Found ((x40 Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found (((x4 Xy000) Xy0) x3) as proof of ((Xp Xy000) Xy0)
% Found x3:((Xr Xx0) Xy0)
% Instantiate: Xy000:=Xy0:a
% Found x3 as proof of ((Xr Xx0) Xy000)
% Found (x400 x3) as proof of ((Xp Xx0) Xy000)
% Found ((x40 Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x4 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found (((x4 Xx0) Xy000) x3) as proof of ((Xp Xx0) Xy000)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x100 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x1 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xx00) Xy0) x50)) as proof of ((Xp Xx00) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x100 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x10 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x1 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x50)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x1 Xy0) Xy000) x50)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xx0) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx00) Xy0)
% Found (x300 x50) as proof of ((Xp Xx00) Xy0)
% Found ((x30 Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (((x3 Xx00) Xy0) x50) as proof of ((Xp Xx00) Xy0)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x3 Xx00) Xy0) x50)) as proof of ((Xp Xx00) Xy0)
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found x50 as proof of ((Xr Xy0) Xy000)
% Found (x300 x50) as proof of ((Xp Xy0) Xy000)
% Found ((x30 Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (((x3 Xy0) Xy000) x50) as proof of ((Xp Xy0) Xy000)
% Found (fun (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x50)) as proof of ((Xp Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> (((x3 Xy0) Xy000) x50)) as proof of (((Xr Xx00) Xy000)->((Xp Xy0) Xy000))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xy0) Xy000)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy000))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy000)))
% Found x5:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x5) as proof of (((Xr Xx0) Xy00)->((Xr Xx00) Xy0))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xy0) Xy00)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found (fun (Xy00:a)=> ((x3 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))->(((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))) (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))) (x50:((Xr Xx0) Xy00))=> x50)))) as proof of (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found x50:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy00))=> x50) as proof of ((Xr Xx0) Xy0)
% Found (fun (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found (fun (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))
% Found (fun (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))
% Found (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50) as proof of (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))
% Found ((conj20 (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (((conj2 (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50)) as proof of ((and (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))))))
% Found (x40 ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found ((x4 (fun (x7:a) (x60:a)=> (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) ((((conj (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))) (a->(a->(a->(((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))->(((Xr Xx0) Xy00)->((Xr Xx0) Xy0))))))) (fun (Xx00:a) (Xy000:a) (x5:((Xr Xx00) Xy000)) (x50:((Xr Xx0) Xy00))=> x50)) (fun (Xx00:a) (Xy000:a) (Xz0:a) (x5:((and (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))) (((Xr Xx0) Xy00)->((Xr Xx0) Xy0)))) (x50:((Xr Xx0) Xy00))=> x50))) as proof of (((Xr Xx0) Xy00)->((Xr Xx0) Xy0))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found x50 as proof of ((Xr Xx0) Xy0)
% Found (x100 x50) as proof of ((Xp Xx0) Xy0)
% Found ((x10 Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (((x1 Xx0) Xy0) x50) as proof of ((Xp Xx0) Xy0)
% Found (fun (x50:((Xr Xx0) Xy000))=> (((x1 Xx0) Xy0) x50)) as proof of ((Xp Xx0) Xy0)
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx0) Xy00)->(forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx0) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x5) as proof of ((Xr Xx0) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (((Xr Xx00) Xy000)->((Xr Xx0) Xy0))
% Found (fun (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found (fun (x5:((Xr Xx0) Xy00)) (Xx00:a) (Xy000:a) (x50:((Xr Xx00) Xy000))=> x5) as proof of (forall (Xx00:a) (Xy000:a), (((Xr Xx00) Xy000)->((Xr Xx0) Xy0)))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx00) Xy000))=> x50) as proof of (((Xr Xx00) Xy000)->((Xr Xy0) Xy000))
% Found x50:((Xr Xx00) Xy000)
% Instantiate: Xy0:=Xy000:a
% Found (fun (x50:((Xr Xx00) Xy000))=> x50) as proof of ((Xr Xx00) Xy0)
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xx00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xy0) Xy00)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy00))))
% Found x5:((Xr Xx00) Xy00)
% Instantiate: Xy0:=Xy00:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x5) as proof of ((Xr Xx00) Xy0)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (((Xr Xx0) Xy000)->((Xr Xx00) Xy0))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x5) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xx00) Xy0)))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))
% Found (fun (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))
% Found x50:((Xr Xx0) Xy000)
% Instantiate: Xy0:=Xx0:a
% Found (fun (x50:((Xr Xx0) Xy000))=> x50) as proof of ((Xr Xy0) Xy000)
% Found (fun (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))
% Found (fun (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found (fun (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))
% Found (fun (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))
% Found (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50) as proof of (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))
% Found ((conj20 (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (((conj2 (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) as proof of ((and (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))))))
% Found (x30 ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50)) (fun (Xx00:a) (Xy00:a) (Xz0:a) (x5:((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x50))) as proof of (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))
% Found ((x3 (fun (x7:a) (x60:a)=> (forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00))))) ((((conj (forall (Xx00:a) (Xy00:a), (((Xr Xx00) Xy00)->(forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))))) (a->(a->(a->(((and (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000)))) (forall (Xy000:a), (((Xr Xx0) Xy000)->((Xr Xy0) Xy000))))->(forall (Xy00:a), (((Xr Xx0) Xy00)->((Xr Xy0) Xy00)))))))) (fun (Xx00:a) (Xy00:a) (x5:((Xr Xx00) Xy00)) (Xy000:a) (x50:((Xr Xx0) Xy000))=> x
% EOF
%------------------------------------------------------------------------------